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Significant figures are critical when reporting scientific data because they give the

reader an idea of how well you could actually measure/report your data. Before

looking at a few examples, let's summarize the rules for significant figures.

1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.

2) ALL zeroes between non-zero numbers are ALWAYS significant.

3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimalpoint AND at the end of the number are ALWAYS significant.

4) ALL zeroes which are to the left of a written decimal point and are in a

number >= 10 are ALWAYS significant.

A helpful way to check rules 3 and 4 is to write the number in scientific notation. If

you can/must get rid of the zeroes, then they are NOT significant.

Scientific Notation:

Scientific Notation

Any quantity can be expressed using a power of ten. As you move the decimal point, you

multiply by 10 as many times as necessary to make the numbers equal. Consider the

following examples:

325 = 32.5 x 10 = 3.25 x 10

1

325 = 3.25 x 10 x 10 = 3.25 x 10

2

325 = 0.325 x 10 x 10 x 10 = 3.25 x 10

3

Because 10

0

= 1 we can also express 325 as 325 x 10

0

.

A number in scientific notation has two parts. The number in front of the x 10 is called

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the coefficient. The power to which 10 is raised is called the exponent.

3.25 x 10

3

The coefficient must have one and only one digit in front of the decimal point. The

exponent will always be a whole number in chemistry, although the exponent can be

fractional number in other disciplines.

There are three rules for using scientific notation:

Rule 1: To express a number in scientific notation, you move the decimal point to

the position such that there is one nonzero digit to the left of the decimal point.

Rule 2: If the decimal point is moved to the left, the exponent is positive.

Rule 3: if the decimal point is moved to the right, the exponent is negative

System of Measurement

Metric and English system of measurement

Prefixes

Table of metric system prefixes, symbols, and multiplication factors.

The metric system defines prefixes and corresponding symbols for positive and

negative powers of 10, as applied to each unit of measure. These prefixes are

defined for one power of ten increments in the more middle range and for three

powers of ten increments in the outlying ranges. For instance, the meter is the

standard unit of length in the metric system. The decimeter is one tenth of ameter, the centimeter is one hundredth of a meter, the millimeter is one

thousandth of a meter, and the micrometer is one millionth of a meter. In

practice, some prefixes and/or combinations are rarely used. The kilometer (one

thousand meters) is a commonly used measure, while the dekameter (ten meters)

and the hectometer (one hundred meters) are rarely used. The prefixes at the top

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and bottom of the table are mostly used in specialized mathematical and

scientific fields.

This convenient table of metric system prefixes is useful when doing metric

conversion calculations.

Metric System Prefix Table

Prefix Symbol Multiplication Factor Power of 10

yotta Y 1,000,000,000,000,000,000,000,000 +24

zetta Z 1,000,000,000,000,000,000,000 +21

exa E 1,000,000,000,000,000,000 +18

peta P 1,000,000,000,000,000 +15

tera T 1,000,000,000,000 +12

giga G 1,000,000,000 +9mega M 1,000,000 +6

kilo k 1,000 +3

hecto h 100 +2

deka da 10 +1

deci d 0.1 -1

centi c 0.01 -2

milli m 0.001 -3

micro 0.000,001 -6

nano n 0.000,000,001 -9

pico p 0.000,000,000,001 -12

femto f 0,000,000,000,000,001 -15

atto a 0,000,000,000,000,000,001 -18

zepto z 0,000,000,000,000,000,000,001 -21

yocto y 0,000,000,000,000,000,000,000,001 -24