1. 1. ʿ F ʾ 1
F ˈ 3 F F
ʿ F
ʿ F
F
ʿ F
2. ʿ ˈ ʿ F 3 F
3. ʿ F F F
3.1 F
3.2
3.3 ʿ F F F
3.4 ʿ F F F F
3.5
3.6
3.7
3.8 F F ʿ

2. F F 3
F
F × F
1. 21× 104
F F F F
. 2.1× 103
. 2.1× 104
. 2.1× 105
. 2.1× 106
2. 42,000 F F F F
. 4.2 × 103
. 4.2 × 104
. 4.2 × 105
. 4.2 × 106
3. 0.05 F F F F
. 5 × 100
. 5 × 10 1−
. 5 × 10 2−
. 5 × 10 3−
4. 0.00000000071 F F F F
. 7.1 × 10 9−
. 7.1 × 10 10−
. 71 × 10 9−
. 71 × 10 11−
5. 9.7 × 104
. 97,000 . 970,000
. 9,700,000 . 97,000,000
6. 2.102 × 106
. 2,102 . 21,020
. 210,200 . 2,102,000
7. 3.67 × 10 5−
. 0.000367 . 0.0000367
. 0.00000367 . 0.000000367

3. 8. ʾ . . 2547 57.4 × 106
A × 10n
1≤ A < 10 n ˈ F F
. 5.74 × 104
. 5.74 × 105
. 5.74 × 106
. 5.74 × 107
9. F 0.000574 × 102
A × 10n
1≤ A < 10 n ˈ F F
. 5.74 × 10 2−
. 5.74 × 10 3−
. 5.74 × 10 4−
. 5.74 × 10 5−
10. ʾ . . 2005 2 × 107
F F
65 F F
. 37,392.31 . 307,692.31
. 3,007,692.31 . 30,739,231

4. F F 3
F
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

5. ʿ F 3
F
F F
1. F F F F F F
F F
2. F F ˆ ˈ F F F

6. F F
(Scientific notation)
F F F
F F F F
- F 2 × 1030
- F 1 3.3 × 10 6−
F 2 × 1030
3.3 × 10 6−
F F ˈ F F F
ˈ ˈ
ˈ
A × 10n
1≤ A < 10 n ˈ
A × 10n
1≤ A < 10 n ˈ F
F F (Scientific notation) F F 2 × 103
, 1 × 106
, 4.109 × 10 6−
1) 2 × 103
n ˈ
A F F F 1 F F F 10
2) 1 × 106
n ˈ
A F F F 1 F F F 10
3) 4.109 × 10 6−
n ˈ
A F F F 1 F F F 10

7. F F F F
A × 10n
1≤ A < 10 n ˈ F F -
F (Scientific notation)

8. ʿ F
3.1
A × 10n
1≤ A < 10 n ˈ
F F F F
F 1) 2 × 10 5−
A = 2
n = -5
1. 1 × 10
A =
n =
2. 2.2 × 102
A =
n =
3. 4.05 × 10 4−
A =
n =
4. 5.4632 × 10 7−
A =
n =
5. 6 × 1024
A =
n =

9. F 2) 1.52 × 103
ˈ F F F
ˈ 1≤ A < 10 n ˈ
F ˈ ...........................................................
6. 0.88 × 10 4−
ˈ F F F
ˈ ............................................................
F ˈ ...........................................................
7. 15.69 × 10 12−
ˈ F F F
ˈ ............................................................
F ˈ ..........................................................
8. 10 × 109
ˈ F F F
ˈ ............................................................
F ˈ ..........................................................
9. 1.32 × 10 7−
ˈ F F F
ˈ ..
F ˈ ..........................................................
10. 2.5 × 10 2
1
ˈ F F F
ˈ ............................................................
F ˈ ...........................................................

10. ʿ F
3.1
F F F F
1. 1× 10
A = 1
n = 1
2. 2.2 × 102
A = 2.2
n = 2
3. 4.05 × 10 4−
A = 4.05
n = -4
4. 5.4632 × 10 7−
A = 5.4632
n = -7
5. 6 × 1024
A = 6
n = 24

11. 6. 0.88 × 10 4−
ˈ F F F
ˈ .................................................
F ˈ A < 1
7. 15.69 × 10 12−
ˈ F F F
ˈ ...................................................
F ˈ A > 10
8. 10 × 109
ˈ F F F
ˈ .....................................................
F ˈ A = 10
9. 1.32 × 10 7−
ˈ F F F
ˈ 1 < A < 10 n ˈ
F ˈ .........................................................
10. 2.5 × 10 2
1
ˈ F F F
ˈ ..........................................................
F ˈ n F ˈ

12. ʿ F
3.2
F ˈ F F F F F
F F F
F 9 × 106
0.25 × 105
( F ) ( F F )
5.67 × 107
0.88 × 10 4−
( ) ( )
15.69 × 10 12−
1.32 × 10 7−
( ) ( )
10 × 109
8.257 × 104
( ) ( )
5 × 10 4−
2.5 × 10 2
1
( ) ( )

13. ʿ F
3.2
F ˈ F F F F F
F F F
5.67 × 107
0.88 × 10 4−
( F ) ( F F )
15.69 × 10 12−
1.32 × 10 7−
( F F ) ( F )
10 × 109
8.257 × 104
( F F ) ( F )
5 × 10 4−
2.5 × 10 2
1
( F ) ( F F )

14. F F
F A × 10n
1≤ A < 10 n ˈ
F F 2 × 1030
, 3.5×1025
, 1.5×108
F F F A × 10n
1≤ A < 10 n ˈ
F
1) 9,000,000 = 9 × 1,000,000
= 9 × (10×10×10×10×10×10)
= 9 × 106
2) 23,500,000 = 235 × 100,000
= 235 × (10×10×10×10×10)
= 235 × 105
= 2.35 × 102
× 105
= 2.35 × 10 52+
= 2.35 × 107
3) 840,000,000,000 = 84 × 10,000,000,000
= 84 × 1010
= 8.4 × 10 × 1010
= 8.4 × 10 101+
= 8.4 × 1011

15. ʿ F
3.3
F F F A × 10n
1≤ A < 10 n ˈ
F 1) 200,000 = 2 × 100,000
= 2 × 105
2) 13.25 × 104
= 1.325 × 10 × 104
= 1.325 × 10 41+
= 1.325 × 105
1. 416.59 × 105
= .
=
= ..
2. 567,000 =
=
=
3. 222.4×107
= ...
=
= ..
4. 87,500,000 =
=
= ..
=
5. 25,645,000,000 = ...
= .
= .
= .

16. ʿ F
3.3
F F F A × 10n
1≤ A < 10 n ˈ
1. 416.59 × 105
= 4.1659 ×102
× 105
= 4.1659 ×10 52+
= 4.1659 ×107
2. 567,000 = 567 × 1,000
= 567 × 103
= 5.67× 102
× 103
= 5.67× 10 52+
= 5.67 × 107
3. 222.4×107
= 2.224 × 102
×107
= 2.224 × 10 72+
= 2.224 × 109
4. 87,500,000 = 875 × 100,000
= 875 × 105
= 8.75 × 102
× 105
= 8.75 × 10 52+
= 8.75 × 107
5. 25,645,000,000 = 25,645 × 1,000,000
= 25,645 × 106
= 2.5645 × 104
× 106
= 2.5645 × 10 64+
= 2.5645 × 1010

17. ʿ F
3.4
F F
F 1) 3.42 × 1012
= 3.42 × 1,000,000,000,000
= 3,420,000,000,000.00
= 3,420,000,000,000
1. 4 × 103
=
= .
= .
2. 2.4 × 105
= .
= ..
= ..
3. 3.123 × 106
= .
= .
= .
4. 4.4567 × 108
=
= .
= .
5. 3.51 × 105
=
= .
= .

18. ʿ F
3.4
F F
1. 4 × 103
= 4 × 1,000
= 4,000
2. 2.4 × 105
= 2.4 × 100,000
= 240,000.0
= 240,000
3. 3.123 × 106
= 3.123 × 1,000,000
= 3,123,000.000
= 3,123,000
4. 4.4567 × 108
= 4.4567 × 100,000,000
= 445,670,000.0000
= 445,670,000
5. 3.51 × 105
= 3.51 × 100,000
= 351,000.00
= 351,000

19. ʿ F
3.5
F F F F
F 3.5 × 105
2.3 × 103
23 × 102
350,000
4.5 × 104
2,035,000,000,000
1.5 × 107
45,000
2.035 × 1012
3,152,000,000,000,000
3.152 × 1015
60,238,000,000,000,000,000,000
6.0238 × 1022
15,000,000
16 × 107
1.25 × 107
125 × 105
5.6 × 106
5,600× 103
4.562 × 109
23.5 × 104
1.6 × 108
45.62 × 108
2.35 × 105

20. ʿ F
3.5
F F F F
4.5 × 104
2,035,000,000,000
1.5 × 107
45,000
2.035 × 1012
3,152,000,000,000,000
3.152 × 1015
60,238,000,000,000,000,000,000
6.0238 × 1022
15,000,000
16 × 107
1.25 × 107
125 × 105
5.6 × 106
5,600× 103
4.562 × 109
23.5 × 104
1.6 × 108
45.62 × 108
2.35 × 105

21. ʿ F
3.6
F F F F
F 52.6× 104
= 5.26 × 105
1. 33 × 103
F
= ..
2. 300 × 106
F
=
3. 503,000,000
=
4. F F 84,960,000
=
5. 30,500,000,000,000,000,000,000
=

22. ʿ F
3.6
F F F F
1. 33 × 103
F
= 3.3 × 104
F
2. 300 × 106
F
= 3 × 108
F
3. 503,000,000
= 5.03 × 108
4. F F 84,960,000
= 8.496 × 107
5. 30,500,000,000,000,000,000,000
= 3.05 × 1022

23. F F F
F A × 10n
1≤ A < 10 n ˈ
F F F F 2 × 10 15−
, 1.7 × 10 3−
, 2.8 × 10 25−
F F F F A × 10n
1≤ A < 10 n ˈ
F
(1) 00090. = 000109 .×
=
00010
1
9
,
×
= 4
10
1
9×
= 4
109 −
×
(2) 0000520. = 00001025 .. ×
=
000100
1
25
,
. ×
=
5
10
1
25 ×.
= 5
1025 −
×.
(3) 0036700000000000. = 00100000000000673 .. ×
=
00000000000010
1
673
,,,,
. ×
=
13
10
1
673 ×.
= 13
10673 −
×.

24. ʿ F
3.7
F A × 10n
1≤ A < 10 n ˈ
F 0.0025 = 2.5 × 0.001
= 2.5 ×
0001
1
,
= 2.5 ×
3
10
1
= 2.5 × 10 3−
1. 0.0001 = ..
= ..
= ..
2. 0.0025 = ..
= ..
= ..
= ..
3. 0.000000009 = ..
= ..
= ..
= ..
4. 0.000000145 = ..
= ..
= ..
= ..
5. 0.00000000008 = ..
= ..
= ..

25. ʿ F
3.7
1. 0.0001 = 1 × 0.0001
= 1 ×
00010
1
,
= 1 × 10 4−
2. 0.0025 = 2.5 × 0.001
= 2.5 ×
0001
1
,
= 2.5 × 3
10
1
= 2.5 × 10 3−
3. 0.000000009 = 9 × 0.000000001
= 9 ×
0000000001
1
,,,
= 9 ×
9
10
1
= 9 × 10 9−
4. 0.000000145 = 1.45 × 0.0000001
= 1.45 ×
00000010
1
,,
= 1.45 ×
7
10
1
= 1.45 × 10 7−
5. 0.00000000008 = 8 × 0.00000000001
= 8 ×
000000000100
1
,,,
= 8 ×
11
10
1
= 8 × 10 11−

26. ʿ F
3.8
F F F F
F 8.1 × 10 3−
= 8.1×
3
10
1
= 8.1 ×
0001
1
,
= 0.0081
1. 6.8 × 10 8−
= .
= .
= .
2. 7.98 × 10 6−
= .
= .
= .
3. 4.5 × 10 8−
= .
= .
= .
4. 7.05 × 10 4−
= .
= .
= .
5. 4.123× 10 5−
=
=
=

27. ʿ F
3.8
1. 6.8 × 10 8−
= 6.8 × 8
10
1
= 6.8 ×
000,000,100
1
= 0.000000068
2. 7.98 × 10 6−
= 7.98 × 6
10
1
= 7.98 ×
000,000,1
1
= 0.00000798
3. 4.5 × 10 8−
= 4.5 × 8
10
1
= 4.5 ×
000,000,100
1
= 0.000000045
4. 7.05 × 10 4−
= 7.05 × 4
10
1
= 7.05 ×
000,10
1
= 0.000705
5. 4.123× 10 5−
= 4.123 × 5
10
1
= 4.123 ×
000,100
1
= 0.00004123

28. ʿ F
3.9
F F F F F
F F F F F
1× 10 13−
= 0.0000000000001
1. 3 × 10 4−
=
2. 915 × 10 9−
=
3. 66 × 10 12−
= ..
4. F ˈ F F 10 × 10 6−
= .
5. 1 F 9 ×10 5−
=

29. ʿ F
3.9
F F F F F
1. 3 × 10 4−
= 0.0003
2. 915 × 10 9−
= 0.000000915
3. 66 × 10 12−
= 0.000000000066
4. F ˈ F F 10 × 10 6−
= 0.00001
5. 1 F 9 ×10 5−
= 0.00009

30. ʿ F
3.10
F F
F F F 232,500 F F F
1.86 × 104
F F F F
F = 232,500 F
= 1.86 × 104
F F
F = 4
1086.1
500,232
×
=
4
5
10861
103252
×
×
.
.
= 1.25 × 10
1.25 × 10
1. ʾ . . 2546 61,800,000
F 4.18×105
F F
F
..........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
2. 3.32×102
3×108
F ˈ F
.........................................................................................................................................
.........................................................................................................................................
.........................................................................................................................................
........................................................................................................................................

31. ʿ F
3.10
1. ʾ . . 2546 61,800,000
F 4.18×105
F F
F
ʾ . .2546 = 61,800,000
= 6.18×107
= 4.18×105
F =
7
5
10186
10184
×
×
.
.
= 0. 68 × 10 2−
0. 68 × 10 2−
2. 3.32×102
F 3×108
F ˈ F
= 3.32×102
F
= 3×108
F
ˈ =
2
8
10323
103
×
×
.
F
= 0.9036× 106
F
0.9036× 106
F

32. F F ʿ F 5
F
F × F
1. 42,000 F F F F
. 4.2 × 103
. 4.2 × 104
. 4.2 × 105
. 4.2 × 106
2. 0.000000888 A × 10n
1≤ A < 10 n ˈ F F
. 8.88× 10 6−
. 8.88× 10 7−
. 8.88× 10 8−
. 8.88× 10 9−
3. 9.7 × 104
. 97,000 . 970,000
. 9,700,000 . 97,000,000
4. (0.0005)2
A × 10n
1≤ A < 10 n ˈ F F
. 2.5×10 8−
. 2.5× 10 6−
. 2.5× 10 7−
. 2.5× 10 5−
5. 2.102 × 106
. 2,102 . 21,020
. 210,200 . 2,102,000
6. 3.67 × 10 5−
. 0.000367 . 0.0000367
. 0.00000367 . 0.000000367
7. 0.05 F F F F
. 5 × 100
. 5 × 10 1−
. 5 × 10 2−
. 5 × 10 3−

33. 8. 0.00000000071 F F F F
. 7.1 × 10 9−
. 7.1 × 10 10−
. 71 × 10 9−
. 71 × 10 11−
9. F ˈ 0.0234× 1010
F F
. 2.34× 105
. 2.34× 106
. 2.34× 107
. 2.34× 108
10. ʾ . . 2005 2 × 107
F F
65 F F
. 307,692.31 . 37,392.31 .
. 3,007,692.31 . 30,739,231
************************

34. F F ʿ F 5
F
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.