1

1

.

.

: 0,1, 2, 3, 4, 5, 6, 7, 8, 9,10, 11, 12, .

. , .

(): 1, 3, 5, 7, 9, 11 ..

(): 0, 2, 4, 6, 8, 10, 12,.

. . .

0,7 -, 0,23 , 0,149 , .. 2,4, 16,38, 3,123.

.. 0,4 0,17 0,12567.

.. 5,133

:

1 = 10 = 100 = 1000 1 = 10 = 100 = 1000

1 = 10 = 100 = 1000 - .

. 10 (10 ) . :

, .

, .

2

, ( ) - . 12,28 = 12,280000 11,200 =11,2. , .

:

1. 0, 1, 2, 3, 4 - .

2. 5, 6, 7, 8, 9 - - .

: , ..., .

,

, , . - .

.

.

. + 12 = 20,

+12 20 . 8 .

, - ' .

.

: 1. , .. 12 +8 =20, 20 12+8 = 8+12 .

3

2. .

, - , :

= + =

: 1. ,

. 2.

.

, - , . .. 3*5 = 5+5+5 = 15 3*5 = 3+3+3+3+3 = 15. 15 5, 3 .

,

.

: 1. 10, 100, 1000 .,

1, 2, 3 . . 2. 10, 100, 1000 .,

1, 2, 3 . . 3. 0,1 0,01 0,001 ., -

1, 2, 3 ., .

3 ,

() : 0.3=0, 1.3=3, 2.3=6, 3.3=9 . 0, 3, 6, 9, 3 -

3 3 = {0, 3, 6, 9, ...}.

= {0, , 2, 3, 4,...}

4

6: 6 = {0, 6, 12, 18, 24, 30, 36, 42, 48 ..} 5: 5 = {0, 5, 10, 15, 20, 25, 30, 35, 40, 45, .} 6 5 : {0, 30, } 30, , : (5, 6) = 30

1, : = . . ...

-

. 2 , 3 . 10 , 1 .

..: 102=100, 103=1000, 104=10.000, 105=100.000.

, : x+x = x (+) x (+)=x+x

, : xx = x () x ()=x x

, ( )

( ) , -.

, , :

: = = . . 0 : = 1, :1 = 0:=0.

, ,

, - , : = . + & <

.

1. 0, . 2. = 0, = . . .

5

&

16: 16 = {1, 2, 4, 8,16}

24: 24 = {1, 2, 3, 4, 6, 8, 12, 24}

16 24 : {1, 2, 4, 8} 8, ,

(16, 24) = 8

10 100 .

10 100 1000 ., . 10, 100, 1000 .

: 260:10 = 26 260:100 = 2,6 260:1000 = 0,26

18,1:10= 1,81 18,1:100 = 0,181 18,1:1000 = 0,0181

1. . .. 7 - , 0, 7, 14, 21, 28,...

2. . .. 27 9, 27 9.

3. , . .. 5 15, , : , 15, 30, 45, 60, ..

4. , . .. 6 18 36, : 18+36 = 54 36-18= 18.

10, 100, ... 10, 100, ..., 1, 2, ...

. 2

2, 0, 2, 4, 6, 8 - . 5

5, 0 5. 3 9

3 9, 3 9.

6

1

2 . :

. , -

1.

!

. ... ... , .

1. ... , , .

2. ... , , .

.. 144 = 24 32, 160 = 25 5, : ... (144, 160) = 25 32 5 = 3295 = 1.440 ... (144, 160) = 24 = 16

, 10 , , - .

: 36,45 : 4,5 = (36,45.10) : (4,510)= 364,5 : 45 = 8

, .

. , - , .

: 70 : 22 = 3,181818.. 70:22 = 3,18.

1 1 . 2 1 .

7

1. .

2. .

1. : . .

. .

. .

2. . .

.

.

.

: 1. : 15+7+12+3+5=42 ( 15+5=20, 7+3=10, 20+10+12=42)

2. : 13 + 2 - 5 + 7= 15 - 5 + 7 = 10 + 7 = 17 13 + 2 - 5 + 7= 15 - 5 + 7 = 15 12 =....

:

. + () -

. - () . [] [] -

. .. 13 + 2 - 5 + 72 = (13+2+7) - (5+2) = 22 7 = 15

3. -:

35+7=15+7=22 35+7=312=36 46 - 54 + 52=24 -20+10 =4+10=14 46 - 54 + 52 = 4192=..... 12:3 + 25 + 3 = 4+10+3=17 12:3 + 25 + 3 = 12:55+3=...

- -

.

8

/ ! 208:4 = 20 (8:4) = 202 = 40 8:420 = (8:4) 20 = 220 = 40 8:420 = 8:80=...

4.

.

(122+8:2)+3 = (24+4)+3 = 28+3=31 (3+5)2 = 82 = 64 (3+5)2 = 32 + 52 = 9+25 =...

5.

.

: 12:3 + 25 + 3 = 4+10+3 = 17 12:3 + 25 + 3 =12:3=4+25=10 .......

, - .

: 9 000 000 = 9106 12 000 000 = 1,2107. -

, 1 10, 10,

10.

/

9

1 1. , ...

:

-

1234,123 1 2 3 4 1 2 3 44,32

0,12345 235.789

44444,44444 21.346,01200 333.123,13 11,34789

0,45

2. . : , -

, , , , , :

5.124,367 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..

7.365,124 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..

2.143,765 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..

4.217,356 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..

3.546,271 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 ..

3. 1 .

23.240,45

90.910,99

43.209,18

11.249,91

77.231,65

27.216,35

97.385,84

10

4. :

5. :

95 (48 31)= (92 43) 24= 69 (18+11)=

(89 18) 14= (55+25) 15= (78 44) +49=

3855 + 9764 2345 1769= 0,234 + 75,32 2,09 11,023=

32,54 13,83 +77,32 2,56= 24,89 + 0,341 5,23 0,28 + 2,01=

6. = 0,01, = 0,1, = 1, = 10, = 100

1456,24 = 2498 = 0,5864 =

7. : ! = () = () 23 5 2= 18 2 15= 250 23,454= 26,175850=

8. :

9 + 45 +212= 318+11 + 42,5= 312,52 53 + 142,5= 27,5 33 + 5,25= 14 32,2 +128= 44,25 11,50,5 + 23,2310=

9. 1.850 3,5 .

225 ;

10. 5 . 8 10

, 12 3 9 11 , 15

75 ;

11. 4 . 16,5 , 14,25

18 . 3,2 ;

356 + 349 =

7356 + 1987 =

1300 + 3357 =

3,567 + 13,023 =

139 + 12,7 =

789,34 + 19,38 =

11

12. .

5 . 6 . -

;

13. :

24 204 0,24 103 1003 0,13

32 302 0,32 15 0,15 0,012

14. . ;

(34)2 (22)3 2333 (22+32) 2223 (43)2 (23)2 (23)3 (2+3)2 25

15. :

5104+2103+8102+5101+4100= 2105+4103+8102+3100=

16. :

(10+8)2 (73)3= (153 18)2 802=

8,42 + (34,57 24,47)3= (33 23)5 (57 37) 3.5= 33+32+31+30= 110+18+16+14+12+10=

152142+132122+112102= (15 14)2+(13 12)2+(11 10)2=

17. :

(7+28+5+13+12) 25= 338+228+178+288= (13,25+26+37,5+23,25) 12,34= 4,835+4,815+2,226,7+2,273,3=

18.

3+4,5+2,5 =2,345 23,67+35+41,33 =0,3456 2+2+7,5+7,5+120+120 +=20

19. 50

40 . ;

20. 36 3 .

2;

12

21. 630 . 3

270 . -

;

22. , = 2 + 4 (-), = 2( + 1) + 6 + 1 ().

23. 60 = 60. ;

24. 33.

;

25. :

] 3 + 45 26= ] 20:2 + 342= ] 48 7 + 311= ]57 23 + 4:2= ] 42:6 + 39 52= ]11526:3+88:11= ] 65:13 + 726 322= ] 712 9 + 124 42:6= ] 1,25 3,4:1,7 + 8= ] 3,3:0,55 + 60,3 + 3,30,2 2=

26. :

] 54:9 + 253 62:12= ] 57 26:16 + 245 + 63= ] 3324 126:9= ] 32 24 + 12:22 + 334= ] 25:8 + 432 18:9= ] 352 532 + 223 28= 27. :

=24,83 + 2323 125:252= =33:11 + 128:42 18:32= =2812:23 + 1113 100 (0,1)2 + 72533=

= 7,32 (23 0,80,5) 0,62 0,127= = (9,6:8 + 0,9) (6:10+42) + 732= = 6,4:22 +(33 +33,3) 72 3220,33= = 132(82 +52)+(52 1294)(12510 542)+13= = 2433 36:223 +(21+24) 32= = 352 532 + 2 (24 8) + 33:9=

28. :

] 1810:2,5 22 (23 7)= ] 72322 32,2 + 25 (3443) + 9= ] 24 (62 + 82) :10 + 2,21,1= ] (6 + 8)2 :(24 23) + (32 8,5)2= ] (0,12 + 0,72) 102 + (2,8 1,2)2= ] (62 + 34 47)59 + (33 +3 39)5=

29. :

=82 + (8)2= =49 + (7)2= =2 + 322 +72= ] =0,9 ] =3,2 ] =3 ( )

13

30. : = 2 + 2 + 2 =( + )2

] =5 & =6 ]=9 & =7 ]=7,3 & =0,1

() , ; -

.

31. :

52 + 62 83 + 32 + 4 3(2 + 6)

3,5

32

0,1

1 . 14

2

: ()

. , . = = =

... 1 .. 0 1 2 3 4 5 6 7 ()

() - .

, - . - 4 , 4, . -: = 4.

. -

. ( ).

, m. m,

000.000.40

1 .

:

(dam) 1 dam = 10 m (hm) 1 hm = 100 m (km) 1 km = 1000 m

: (dm) 1 dm = 1/10 m (cm) 1 cm = 1/100 m (mm) 1mm = 1/1000 m

:

(yrd), 3 (ft) 1 12 (in). O 0,75m = 75 cm. 1609 m 1852 m 15,43 m (1 = 120 )

1 . 15

: , , , ( ), . - () -

.

- :

7,8 m

x 10 m 7,8 m

78 dm x 10 dm : 10 78 dm

780 cm

x 10 cm : 10 780 cm

7.800 mm mm : 10 7.800 mm

-

( ) . - , . - , .

-

. ( ).

, m2. 1 m. :

. (dam2) 1 dam2 = 100 m2 ( ) . (hm2) 1 hm2 = 10.000 m2 ( ) . (km2) 1 km2 = 100.000 m2

: . (dm2) 1 dm2 = 1/100 m2 . (cm2) 1 cm2 = 1/10.000 m2 . (mm2) 1mm2 = 1/1.000.000 m2

: 1 = 1000 m2 ( ).

m2 :

1 . 16

7,8 m2

x 100 m2 7,8 m2

780 dm2

x 100 dm2 : 100 780 dm2

78.000 cm2

x 100 cm2 : 100 78.000 cm2

7.800.000 mm2 mm2 : 100 7.800.000 mm2

, -, .

. -

, . ..: = 6m = 2m, E = = 6m2m =12 m2

- , .

..: = 6m , E = (= 2) = 6m6m =36 m2

, .

, ( ) . - ( ) .

-

. ( ). , m3.

1 m.

(dam3) 1 dam3 = 1.000 m3 (hm3) 1 hm3 = 1.000.000 m3 (km3) 1 km3 = 1.000.000.000 m3

1 . 17

(dm3) 1 dm2 = 1/1.000 m2 (cm3) 1 cm2 = 1/1.000.000 m2 (mm2) 1mm2 = 1/1.000.000.000 m2

(l), 1l = 1.000ml.

1dm3. ml=1cm2

.

! , ;

m3 - :

7,8 m3

x 1.000 m3 7,8 m3

7.800 dm3

x 1.000 dm3 : 1.000 7.800 dm3

7.800.000 cm3

x 1.000 cm3 : 1.000 7.800.000 cm3

7.800.000.000 mm3 mm3 : 1.000 7.800.000.000 mm3

, - - . ,

, V = ,

, V = = 3 .

(sec).

(min) 1min = 60 sec (h) 1h = 60 min = 3.600 sec.

(d) 1d = 24 h 1 =

365 366 , , 1 = 100 .

( ) (Kg). O (ton) 1ton = 1.000Kg. (gr), 1.000 gr = 1Kg.

. ; ( -)

1 . 18

2001 ().

1/1/2002 , ().

100 : ) : 1, 2, 5, 10, 20, 50 , 1 & 2 ) : 5, 10, 20, 50, 100, 200, 500.

,

!

1 . 19

1. 6,4 m 25 dm

3850 mm. (. 61,6 m3) 2. 28dm ] m 3, ] dm3, ] cm 3 (. 21,952m3, 21.952dm3, 21.952.000cm3) 3. 64 . . (V=512 m3) 4. 70 dm, 5 m. 217

m3, . (=6,2 ) 5. 2,9 ,

1,5 0,72 . 1725 ;

(. 3.132 l 5.402.700 ) 6. 1,8 m ,

1,2 m 8,5 dm, 37cm, 15 cm , 17 cm. ; (. 195 /)

7. 8 m3 .

34 6,5 m 3,5 m. (. 11,956 m)

8. 80 cm,

45cm 60 cm. ] . ] 120 ;

(. 216dm3, 33,33 cm ) 9. 184.800 . 15,4 . 7000 , ;

(. 84.000 ) 10. : 10 cm, 5 cm

13,2 cm. 0,1 dm ;

(. 3,2 cm ) 11. . : ] . ] . (. 8, 27)

1 . 20

. 1. 0,68m 50cm. (. =2,36 m, =0,34 m2 ) 2. 1,28 km 360m.

, . (. =280m, E=100800m2)

3. 7,8 m 50,7 m2.

. (. 6,5m, =28,6m) 4. 36,8m. (. =84,64m2) 5. 20 . -

25 , . (. 16 ) 6. 65dm 3,4 m 25.480 . -

; ( . 563.108 ) 7. 6

3,6 . 40 cm. 856 ; (. 135 , 115.560 )

8. 48,5 250.000

1.455.000 . . (. =5820 m2, =120 m)

9. 120 m 6240 m2 . -

. ; (. 3.536 m2)

10.

80 . 45.000 . (. =256m2, 11.520.000 drx)

11. 70 m

150 cm. - 50 cm 30 cm.

(. 2.860 ) 12. , 88 dam.