5 decimals, arithmetic of decimals
TRANSCRIPT
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Decimals
Back to Algebra–Ready Review Content.
![Page 2: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/2.jpg)
DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system.
![Page 3: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/3.jpg)
$100’s $1’s$10’s
DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Let’s demonstrate this with a cash register that holds $1’s, $10’s, $100’s, ...etc.
*
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$100’s $1’s$10’s
DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Let’s demonstrate this with a cash register that holds $1’s, $10’s, $100’s, ...etc. For a moment let’s assume that US Treasury not only makes
*
(dime),101$ (penny),100
1$
, a “itty”, and10001$ , a “bitty”, etc...10000
1$
but also makes smaller value coins
of
![Page 5: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/5.jpg)
$100’s $1’s$10’s
DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Let’s demonstrate this with a cash register that holds $1’s, $10’s, $100’s, ...etc. For a moment let’s assume that US Treasury not only makes
*
dimes
101
$
pennies itties
1001
$ 10001
$
(dime),101$ (penny),100
1$
, a “itty”, and10001$ , a “bitty”, etc...10000
1$
but also makes smaller value coins
100001
$
of
bitties
*
![Page 6: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/6.jpg)
$100’s $1’s$10’s
DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Let’s demonstrate this with a cash register that holds $1’s, $10’s, $100’s, ...etc. For a moment let’s assume that US Treasury not only makes
* 101
$ 1001
$ 10001
$
(dime),101$ (penny),100
1$
, a “itty”, and10001$ , a “bitty”, etc...10000
1$
but also makes smaller value coins
100001
$
of
Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc...
*
dimes pennies itties bitties
![Page 7: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/7.jpg)
$100’s $1’s$10’s
DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Let’s demonstrate this with a cash register that holds $1’s, $10’s, $100’s, ...etc. For a moment let’s assume that US Treasury not only makes
* 101
$ 1001
$ 10001
$
(dime),101$ (penny),100
1$
, a “itty”, and10001$ , a “bitty”, etc...10000
1$
but also makes smaller value coins
Let’s further assume each slot only hold up to 9 bills or coinsso we may record the money stored in the register
100001
$
of
Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc...
*
dimes pennies itties bitties
![Page 8: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/8.jpg)
$100’s $1’s$10’s
DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Let’s demonstrate this with a cash register that holds $1’s, $10’s, $100’s, ...etc. For a moment let’s assume that US Treasury not only makes
* 101
$ 1001
$ 10001
$
(dime),101$ (penny),100
1$
, a “itty”, and10001$ , a “bitty”, etc...10000
1$
# # # # ##
but also makes smaller value coins
Let’s further assume each slot only hold up to 9 bills or coinsso we may record the money stored in the register
100001
$
of
Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc...
#
*
dimes pennies itties bitties
![Page 9: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/9.jpg)
$100’s $1’s$10’s
Arithmetic of DecimalsIn order to track smaller and smaller quantities we include base-10 fractions to the whole number-system. Let’s demonstrate this with a cash register that holds $1’s, $10’s, $100’s, ...etc. For a moment let’s assume that US Treasury not only makes
* 101
$ 1001
$ 10001
$
(dime),101$ (penny),100
1$
, a “itty”, and10001$ , a “bitty”, etc...10000
1$
# # # # ##
simply as . # # # # where the #’s = 0,1,.., or 9. # # #
The decimal point (the divider)
but also makes smaller value coins
Let’s further assume each slot only hold up to 9 bills or coinsso we may record the money stored in the register
100001
$
of
Note that 10 itties = 1 penny and 10 bitties = 1 itty, etc...
#
*
dimes pennies itties bitties
.
![Page 10: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/10.jpg)
$100’s* $1’s$10’s* 101
$ 1001
$ 10001
$
4 5 63
For example,
.
Decimals
dimes pennies itties bitties
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$100’s* $1’s$10’s*
dimes
101
$
pennies itties
1001
$ 10001
$
4 5 63
For example,
. 43 5 6is written as
.
Decimals
bitties
![Page 12: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/12.jpg)
$100’s* $1’s$10’s*
dimes
101
$
pennies itties
1001
$ 10001
$
4 5 63
For example,
. 43 5 6is written as
.
4 $1’s3 $10’s
Decimals
bitties
![Page 13: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/13.jpg)
$100’s* $1’s$10’s*
dimes
101
$
pennies itties
1001
$ 10001
$
4 5 63
For example,
. 43 5 6is written as
.
4 $1’s3 $10’s
(5 dimes)(6 pennies)
105 100
6$$
Decimals
bitties
![Page 14: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/14.jpg)
$100’s* $1’s$10’s*
dimes
101
$
pennies itties
1001
$ 10001
$
4 5 63
For example,
. 43 5 6is written as
.
4 $1’s3 $10’s
(5 dimes)(6 pennies)
105 100
6$$
$100’s $1’s$10’s* 101
$ 1001
$ 10001
$
4 5 0 7
Decimals
8
100001$
bitties
.
![Page 15: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/15.jpg)
$100’s* $1’s$10’s*
dimes
101
$
pennies itties
1001
$ 10001
$
4 5 63
For example,
. 43 5 6is written as
.
4 $1’s3 $10’s
(5 dimes)(6 pennies)
105 100
6$$
$100’s $1’s$10’s* 101
$ 1001
$ 10001
$
4 5 0 7
4 $1’s
4is written as .
Decimals
8
100001$
bitties
.
![Page 16: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/16.jpg)
$100’s* $1’s$10’s*
dimes
101
$
pennies itties
1001
$ 10001
$
4 5 63
For example,
. 43 5 6is written as
.
4 $1’s3 $10’s
(5 dimes)(6 pennies)
105 100
6$$
$100’s $1’s$10’s*
dimes
101
$
pennies itties
1001
$ 10001
$
4 5 0 7
4 $1’s (no penny)1000$
(5 dimes)105$
10007$
4 75 0is written as .
Decimals
8
100001$
(8 bitties)100008
$
bitties
.
8
(7 itties)
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Comparing Decimal NumbersDecimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.)
![Page 18: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/18.jpg)
Comparing Decimal Numbers
Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.)
![Page 19: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/19.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points,
Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
![Page 20: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/20.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points,
Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
0.00980.0100.00199
1. line up by the decimal points
![Page 21: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/21.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right,
Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
0.00980.0100.00199
1. line up by the decimal points
![Page 22: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/22.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right,
Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
0.00980.0100.00199
1. line up by the decimal points
2. scan the digits in each slot from left to right
![Page 23: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/23.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, 3. the one with the 1st largest digit is the largest quantity.Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
0.00980.0100.00199
1. line up by the decimal points
2. scan the digits in each slot from left to right
![Page 24: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/24.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, 3. the one with the 1st largest digit is the largest quantity.Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
0.00980.0100.00199
1. line up by the decimal points
2. scan the digits in each slot from left to right
1st largest digit, so it’s the largest number
![Page 25: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/25.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, 3. the one with the 1st largest digit is the largest quantity.Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
0.00980.0100.00199
1. line up by the decimal points
2. scan the digits in each slot from left to right
1st largest digit, so it’s the largest number
2nd largest digit, so it’s the 2nd largest number
![Page 26: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/26.jpg)
Comparing Decimal Numbers
1. line up the numbers by their decimal points, 2. scan the digits, i.e. the number of coins, in the slot from left to right, 3. the one with the 1st largest digit is the largest quantity.Example A. List 0.0098, 0.010, 0.00199 from the largest to the smallest.
Decimals
Because decimal numbers may be viewed as coins stored in a base-10 cash registers, therefore to determine which decimal numbers is the largest is similar to finding which cash register contains more money (in coins.) Specifically, to compare multiple decimal numbers to see which is largest, we
0.00980.0100.00199
1. line up by the decimal points
2. scan the digits in each slot from left to right
1st largest digit, so it’s the largest number
2nd largest digit, so it’s the 2nd largest number
So listing them from the largest to the smallest, we have:0.010, 0.0098, 0.00199.
![Page 27: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/27.jpg)
Here are the official names of some of the base-10-denominator fractions. Note the suffix “ ’th ” at the end their names.
1’s 10 100 1,000 10,000 100,0001 1 1 1 1
1,000,0001
Decimals
10’s
ones tenths hundredths thousandthsten–thousandths
Decimal point
hundred–thousandths millionths.tens
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Here are the official names of some of the base-10-denominator fractions. Note the suffix “ ’th ” at the end their names.
1’s 10 100 1,000 10,000
ones tenths hundredths thousandthsten–thousandths
100,000
Decimal point
hundred–thousandths millionths.
1 1 1 1 11,000,000
1
Hence
2 . 3 4 5 6 7is 2 + 10 100 1,000 10,000 100,000
3 4 5 6 7+ + + +
Threetenths
Fourhundredths
Fivethousandths
Six ten-thousandths
Seven hundred-thousandth
Decimals
10’s
tens
Two
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Here are the official names of some of the base-10-denominator fractions. Note the suffix “ ’th ” at the end their names.
In fraction it’s 2 100,00034,567
Decimals
Hence
2 . 3 4 5 6 7is 2 + 10 100 1,000 10,000 100,000
3 4 5 6 7+ + + +
Threetenths
Fourhundredths
Fivethousandths
Six ten-thousandths
Seven hundred-thousandth
1’s 10 100 1,000 10,000
ones tenths hundredths thousandthsten–thousandths
100,000
Decimal point
hundred–thousandths millionths.
1 1 1 1 11,000,000
110’s
tens
.
Two
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DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual.
Example D. a. Add 8.978 + 0.657
![Page 31: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/31.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual.
Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
.
![Page 32: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/32.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual. Do the same for subtracting decimals.Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
1
53
1
6
1
9 .
![Page 33: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/33.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual. Do the same for subtracting decimals.Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
1
53
1
6
1
9So the sum is 9.635. .
![Page 34: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/34.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual. Do the same for subtracting decimals.Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
1
53
1
6
1
9So the sum is 9.635. .
b. Subtract 0.078 – 0.0293
![Page 35: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/35.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual. Do the same for subtracting decimals.Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
1
53
1
6
1
9So the sum is 9.635. .
b. Subtract 0.078 – 0.0293
0 . 0 7 80 . 0 2 9 3 –
.
![Page 36: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/36.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual. Do the same for subtracting decimals.Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
1
53
1
6
1
9So the sum is 9.635. .
b. Subtract 0.078 – 0.0293
0 . 0 7 80 . 0 2 9 3 –
0
Add 0’s at the end of the decimal expansion,then subtract
.
![Page 37: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/37.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual. Do the same for subtracting decimals.Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
1
53
1
6
1
9So the sum is 9.635. .
b. Subtract 0.078 – 0.0293
0 . 0 7 80 . 0 2 9 3 –
8400 . 7
0
Add 0’s at the end of the decimal expansion,then subtract
![Page 38: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/38.jpg)
DecimalsTo add decimal numbers, we line up the decimal point the set the its position then add as usual. Do the same for subtracting decimals.Example D. a. Add 8.978 + 0.657
8 . 9 7 80 . 6 5 7 +
1
53
1
6
1
9So the sum is 9.635. .
b. Subtract 0.078 – 0.0293
0 . 0 7 80 . 0 2 9 3 –
8400 . 7
0
Hence 0.078 – 0.0293 = 0.0487.
Add 0’s at the end of the decimal expansion,then subtract.
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47
7x
9
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
6
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we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
9For example,
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
6
![Page 41: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/41.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
4x7=28
9For example,
6
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 42: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/42.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
8
record the 8
carry the 2
4x7=28
9For example,
6
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 43: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/43.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
8
record the 8
carry the 2
4x7=28 7x7=49,
9For example,
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
6
![Page 44: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/44.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
8
record the 8
carry the 2
4x7=28 7x7=49, 49+2=51
9For example,
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
6
![Page 45: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/45.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
8
record the 8
carry the 2
4x7=28 7x7=49,
1
record the 1
49+2=51
9For example,
carry the 5
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
6
![Page 46: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/46.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
8
record the 8
carry the 2
4x7=28 7x7=49,
1
record the 1
carry the 5
49+2=51
9
9x7=63, 63+5= 68
For example,
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
6
![Page 47: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/47.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
8
record the 8
carry the 2
4x7=28 7x7=49,
1
record the 1
carry the 5
49+2=51
9
9x7=63, 63+5= 68
8
record the 8
carry the 6
6
For example,
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
6
![Page 48: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/48.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.
47
7x
8
record the 8
carry the 2
4x7=28 7x7=49,
1
record the 1
carry the 5
49+2=51
9
9x7=63, 63+5= 68
8
record the 8
carry the 6
6When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example,
6
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 49: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/49.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example, 47
78
record the 8
1
record the 1
9
8
record the 8
carry the 6
6
6x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 50: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/50.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example, 47
78
record the 8
4x6=24
1
record the 1
9
8
record the 8
carry the 6
6
6
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 51: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/51.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example, 47
78
record the 8
4x6=24
1
record the 1
←record
9
8
record the 8
carry the 6
6
6
carry the 2
4
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 52: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/52.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example, 47
78
record the 8
4x6=24 7x6=42,
1
record the 1
←record
42+2=44
9
8
record the 8
carry the 6
6
6
carry the 2
4
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 53: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/53.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example, 47
78
record the 8
carry the 4
4x6=24 7x6=42,
1
record the 1
←record
42+2=44
9
8
record the 8
carry the 6
6
6
carry the 2
44
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 54: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/54.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example, 47
78
record the 8
carry the 4
4x6=24 7x6=42,
1
record the 1
←record
42+2=44
9
9x6=54 54+4= 58
8
record the 8
carry the 6
6
6
carry the 2
44
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 55: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/55.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example, 47
78
record the 8
carry the 4
4x6=24 7x6=42,
1
record the 1
←record
42+2=44
9
9x6=54 54+4= 58
8
record the 8
carry the 6
6
6
carry the 2
4485
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 56: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/56.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example,
Because we are in a place value system, the result of the multiplication must be placed in the correct slots, so it is shift one place to the left.
47
78
record the 8
carry the 4
4x6=24 7x6=42,
1
record the 1
←record
42+2=44
9
9x6=54 54+4= 58
8
record the 8
carry the 6
6
6
carry the 2
Finally, we obtain the answer by adding the two columns.
4485+
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 57: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/57.jpg)
we start the multiplication by multiplying the top with the bottom right most digit.When this is completed, we proceed with the multiplication to the next digit of the bottom number.
For example,
Because we are in a place value system, the result of the multiplication must be placed in the correct slots, so it is shift one place to the left.
47
78
record the 8
carry the 4
4x6=24 7x6=42,
1
record the 1
←record
42+2=44
9
9x6=54 54+4= 58
8
record the 8
carry the 6
6
6
carry the 2
Finally, we obtain the answer by adding the two columns.
44
85
85 2 6 5
+
x
Let's review the multiplication of two multiple digit numbers. Such a problem is treated as multiple problems of multiplying with a single digit number.
Multiplication and Division of Decimals
![Page 58: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/58.jpg)
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer.
Multiplication and Division of Decimals
![Page 59: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/59.jpg)
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer.
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7
![Page 60: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/60.jpg)
47781
9
866
4485
85 2 6 5
x
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer.
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7Ignore the decimal points and multiply 974 x 67 = 65258.
![Page 61: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/61.jpg)
I. count the total number of places to the right of the decimal point in both decimal numbers,
47781
9
866
4485
85 2 6 5
x
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7Ignore the decimal points and multiply 974 x 67 = 65258. Put back the decimal points to count the number of places after them, which is 3.
![Page 62: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/62.jpg)
I. count the total number of places to the right of the decimal point in both decimal numbers,
47781
9
866
4485
85 2 6 5
x
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7Ignore the decimal points and multiply 974 x 67 = 65258. Put back the decimal points to count the number of places after them, which is 3.
..
There are 3 places after the decimal point
![Page 63: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/63.jpg)
I. count the total number of places to the right of the decimal point in both decimal numbers, II. take the decimal point at the right end of their product, count to the left the same total–number of places, to place the decimal point.
47781
9
866
4485
85 2 6 5
x
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7.
.There are 3 places after the decimal point
Ignore the decimal points and multiply 974 x 67 = 65258. Put back the decimal points to count the number of places after them, which is 3.
![Page 64: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/64.jpg)
I. count the total number of places to the right of the decimal point in both decimal numbers, II. take the decimal point at the right end of their product, count to the left the same total–number of places, to place the decimal point.
47781
9
866
4485
85 2 6 5
x
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7.
.There are 3 places after the decimal point
Move the decimal point of the product3 places to the left for the answer.
Ignore the decimal points and multiply 974 x 67 = 65258. Put back the decimal points to count the number of places after them, which is 3.
![Page 65: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/65.jpg)
I. count the total number of places to the right of the decimal point in both decimal numbers, II. take the decimal point at the right end of their product, count to the left the same total–number of places, to place the decimal point.
47781
9
866
4485
5 2 6 5
x
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7.
.There are 3 places after the decimal point
Move the decimal point of the product3 places to the left for the answer.
So move the decimal point 3 places left.
.. 8
Ignore the decimal points and multiply 974 x 67 = 65258. Put back the decimal points to count the number of places after them, which is 3.
![Page 66: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/66.jpg)
I. count the total number of places to the right of the decimal point in both decimal numbers, II. take the decimal point at the right end of their product, count to the left the same total–number of places, to place the decimal point.
47781
9
866
4485
5 2 6 5
x
To multiply two decimal numbers, do exactly the same–then insert the decimal point in the product at the correct place for the final answer. To locate the position of the decimal point:
Multiplication and Division of Decimals
Example E. Multiply 9.74 x 6.7.
.There are 3 places after the decimal point
Move the decimal point of the product3 places to the left for the answer.
So move the decimal point 3 places left.
.. 8
Hence 9.74 x 6.7 = 65.258
Ignore the decimal points and multiply 974 x 67 = 65258. Put back the decimal points to count the number of places after them, which is 3.
![Page 67: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/67.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
Remove the trailing 0’s to the right for the multiplication decimal numbers.
b. Multiply 0.00012 x 0.00700.
![Page 68: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/68.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700
b. Multiply 0.00012 x 0.00700.
![Page 69: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/69.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
b. Multiply 0.00012 x 0.00700.
![Page 70: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/70.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
b. Multiply 0.00012 x 0.00700.
![Page 71: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/71.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84.
b. Multiply 0.00012 x 0.00700.
![Page 72: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/72.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84. So move the decimal point two places left to place the decimal point.
0. 8 4.
b. Multiply 0.00012 x 0.00700.
![Page 73: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/73.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84. So move the decimal point two places left to place the decimal point.
0. 8 4.
b. Multiply 0.00012 x 0.00700.
![Page 74: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/74.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84. So move the decimal point two places left to place the decimal point.
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.
8 4.
![Page 75: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/75.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84. So move the decimal point two places left to place the decimal point.
8 4. = 12 x 7
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.There are eight places after the decimal points so move the point eight place left and fill in 0’s as we move:
8 4.
![Page 76: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/76.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84. So move the decimal point two places left to place the decimal point.
8 4. = 12 x 7
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.There are eight places after the decimal points so move the point eight place left and fill in 0’s as we move:
8 4.
0. 0 0 0 0 0 0
8 places
![Page 77: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/77.jpg)
Multiplication and Division of Decimals
Example F. a. Multiply 1.200 x 0.700
So 1.200 x 0.700 = 0.84
b. Multiply 0.00012 x 0.00700.
There are two places after the decimal points.
Remove the trailing 0’s to the right for the multiplication decimal numbers.
We can drop the extra trailing 0’s in 1.200 x 0.700 = 1.2 x 0.7.
Multiply 12 x 7 = 84. So move the decimal point two places left to place the decimal point.
8 4. = 12 x 7
0.
0.00012 x 0.00700 = 0.00012 x 0.007 and 12 x 7 = 84.There are eight places after the decimal points so move the point eight place left and fill in 0’s as we move:
8 4.
0. 0 0 0 0 0 0
8 placesHence 0.00012 x 0.00700 = 0.00000084.
![Page 78: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/78.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual
651.3
![Page 79: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/79.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual
651.3
= 1.3 ÷ 65651.3Calculate
by long division.
![Page 80: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/80.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual
651.3
)6 5 1 . 3 = 1.3 ÷ 65651.3Calculate
by long division.
![Page 81: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/81.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3.
= 1.3 ÷ 65651.3Calculate
by long division. the decimal point place
![Page 82: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/82.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 30 . 0
= 1.3 ÷ 65651.3Calculate
by long division. the decimal point place
![Page 83: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/83.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3 00 . 0
= 1.3 ÷ 65651.3Calculate
by long division. the decimal point place
Pack trailing 0’s so it’s enough to enter a quotient
![Page 84: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/84.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3 01 3 0
2.
0
= 1.3 ÷ 65651.3Calculate
by long division. the decimal point place
00 Pack trailing 0’s so it’s enough to enter a quotient
![Page 85: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/85.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3Calculate
by long division. the decimal point place
00 Pack trailing 0’s so it’s enough to enter a quotient
![Page 86: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/86.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
Example H. a. Compute 0.0013 ÷ 0.00065
We change a problem of dividing two decimal numbers to a problem that is a decimal number divided by an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3Calculate
by long division.
00
the decimal point place
Pack trailing 0’s so it’s enough to enter a quotient
![Page 87: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/87.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
Example H. a. Compute 0.0013 ÷ 0.00065
We change a problem of dividing two decimal numbers to a problem that is a decimal number divided by an integer. Write the problem as a fraction then move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3Calculate
by long division.
0.000650.0013
Write 0.0013 ÷ 0.00065 as
00
the decimal point place
Pack trailing 0’s so it’s enough to enter a quotient
![Page 88: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/88.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
Example H. a. Compute 0.0013 ÷ 0.00065
.
move 5 places so the numerator is an integer.
We change a problem of dividing two decimal numbers to a problem that is a decimal number divided by an integer. Write the problem as a fraction then move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3Calculate
by long division.
0.000650.0013
Write 0.0013 ÷ 0.00065 as .
= .
6513
. 0 0
00
the decimal point place
Pack trailing 0’s so it’s enough to enter a quotient
![Page 89: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/89.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
Example H. a. Compute 0.0013 ÷ 0.00065
.
move 5 places so the numerator is an integer.
We change a problem of dividing two decimal numbers to a problem that is a decimal number divided by an integer. Write the problem as a fraction then move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3Calculate
by long division.
0.000650.0013
Write 0.0013 ÷ 0.00065 as
= .
6513
. 0 0 = 2
Hence 0.0013 ÷ 0.00065 = 2
00
the decimal point place
Pack trailing 0’s so it’s enough to enter a quotient
.
![Page 90: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/90.jpg)
Multiplication and Division of Decimals
Example G. Compute by long division.
To divide a decimal number by an integer, do long division as usual and leave the decimal point in the same position for the quotient .
Example H. a. Compute 0.0013 ÷ 0.00065
.
move 5 places so the numerator is an integer.
We change a problem of dividing two decimal numbers to a problem that is a decimal number divided by an integer. Write the problem as a fraction then move the decimal points in tandem until the numerator is an integer.
651.3
)6 5 1 . 3 01 3 0
2.
0Hence 1.3 ÷ 65 = 0.02
= 1.3 ÷ 65651.3Calculate
by long division.
0.000650.0013
Write 0.0013 ÷ 0.00065 as
= .
6513
. 0 0 = 2
Hence 0.0013 ÷ 0.00065 = 2
00
the decimal point place
Pack trailing 0’s so it’s enough to enter a quotient
.
![Page 91: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/91.jpg)
Multiplication and Division of DecimalsExample H. b. Compute 0.00013 ÷ 0.65
![Page 92: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/92.jpg)
Multiplication and Division of DecimalsExample H. b. Compute 0.00013 ÷ 0.65
0.650.00 013
Write 0.00013 ÷ 0.65 as
![Page 93: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/93.jpg)
Multiplication and Division of DecimalsExample H. b. Compute 0.00013 ÷ 0.65
. move 2 places
0.650.00 013
Write 0.00013 ÷ 0.65 as .
= . 650 013.
![Page 94: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/94.jpg)
Multiplication and Division of DecimalsExample H. b. Compute 0.00013 ÷ 0.65
. move 2 places
)65 0 .1 3
0.650.00 013
Write 0.00013 ÷ 0.65 as .
= . 650 013.
Calculate this by long division:
![Page 95: 5 decimals, arithmetic of decimals](https://reader035.vdocuments.pub/reader035/viewer/2022062216/55cff4c1bb61eba96e8b461a/html5/thumbnails/95.jpg)
Multiplication and Division of DecimalsExample H. b. Compute 0.00013 ÷ 0.65
. move 2 places
)65 0 .1 3 01 3 0
0 20 . 0
0
0.650.00 013
Write 0.00013 ÷ 0.65 as .
= . 650 013.
Hence 0.0013 ÷ 0. 65 = 0.002.
Calculate this by long division: