O-LEVEL
MATHEMATICS
SCIENTIFIC NOTATION AND STANDARD
FORM
Muhammad Javed Iqbal
Page 1 of 31
Name :
Score :
Scientific Notation
Example:
Write 3200 in scientific notation.
3 2 0 0.
We should move the decimal point 3 places to the left. So, the exponent will be 3.
3, 200 = 3.2 × 103
Express each number in scientific notation.
1)
625
=
2)
4, 216
=
3) 49, 603 =
4)
25
=
5) 18, 569 =
6)
836
=
7) 9, 364
=
8)
34, 121 =
9)
=
10)
912
=
=
12)
4, 874
=
22
11) 7, 350
13) 62, 503 =
Muhammad Javed Iqbal
14) 13, 058 =
Page 2 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 985625 in scientific notation.
9 8 5 6 2 5.
We should move the decimal point 5 places to the left. So, the exponent will be 5.
985, 625 = 9.85625 × 105
Express each number in scientific notation.
1) 7, 250, 000, 000
=
2) 872, 000, 000, 000, 000 =
3) 110, 000, 000
=
4) 90, 500, 000, 000
=
5) 28, 189, 000, 000, 000
=
6) 5, 620, 000
=
7) 874, 020, 000, 000
=
8) 14, 000, 000
=
9) 7,586, 000, 000, 000, 000 =
10) 4, 460, 500, 000, 000
Muhammad Javed Iqbal
=
Page 3 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 659172 in scientific notation.
6 5 9 1 7
2.
We should move the decimal point 5 places to the left. So, the exponent will be 5.
659, 172 = 6.59172 × 105
Express each number in scientific notation.
1) 480, 000, 000, 000
=
2) 100, 000, 000, 000, 000 =
3) 9, 520, 000
=
4) 3, 200, 000, 000
=
5) 7, 285, 700, 000, 000
=
6) 247, 000, 000
=
7) 50, 423, 000, 000, 000
=
8) 13, 425, 000
=
9) 642, 000, 000, 000, 000 =
10) 99, 522, 000, 000
Muhammad Javed Iqbal
=
Page 4 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 3200 in scientific notation.
3 2 0 0.
We should move the decimal point 3 places to the left. So, the exponent will be 3.
3, 200 = 3.2 × 103
Express each number in scientific notation.
1)
625
=
2)
4, 216
=
3) 49, 603 =
4)
25
=
5) 18, 569 =
6)
836
=
7) 9, 364
=
8)
34, 121 =
9)
=
10)
912
=
=
12)
4, 874
=
22
11) 7, 350
13) 62, 503 =
Muhammad Javed Iqbal
14) 13, 058 =
Page 5 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 985625 in scientific notation.
9 8 5 6 2 5.
We should move the decimal point 5 places to the left. So, the exponent will be 5.
985, 625 = 9.85625 × 105
Express each number in scientific notation.
1) 7, 250, 000, 000
=
2) 872, 000, 000, 000, 000 =
3) 110, 000, 000
=
4) 90, 500, 000, 000
=
5) 28, 189, 000, 000, 000
=
6) 5, 620, 000
=
7) 874, 020, 000, 000
=
8) 14, 000, 000
=
9) 7,586, 000, 000, 000, 000 =
10) 4, 460, 500, 000, 000
Muhammad Javed Iqbal
=
Page 6 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 659172 in scientific notation.
6 5 9 1 7
2.
We should move the decimal point 5 places to the left. So, the exponent will be 5.
659, 172 = 6.59172 × 105
Express each number in scientific notation.
1) 480, 000, 000, 000
=
2) 100, 000, 000, 000, 000 =
3) 9, 520, 000
=
4) 3, 200, 000, 000
=
5) 7, 285, 700, 000, 000
=
6) 247, 000, 000
=
7) 50, 423, 000, 000, 000
=
8) 13, 425, 000
=
9) 642, 000, 000, 000, 000 =
10) 99, 522, 000, 000
Muhammad Javed Iqbal
=
Page 7 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 8.821 × 102 in standard notation.
Here the exponent is 2. We should move the decimal point 2 places to the right.
8.8 2 1
8.821 × 102 = 882.1
Express each number in standard notation.
1) 7.452 × 10
=
2)
1.9824 × 104 =
3) 5.9004 × 104
=
4)
5.237 × 103
=
5) 8.15 × 102
=
6)
9.011 × 102
=
7) 6.1425 × 103
=
8) 1.4592 × 105
=
9) 3.1478 × 104
=
10)
6.982 × 103
=
11) 7.586 × 10
=
12) 1.1286 × 104
=
13) 4.7126 × 103
=
14) 9.14 × 102
=
Muhammad Javed Iqbal
Page 8 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 2.97853 × 105 in standard notation.
Here the exponent is 5. We should move the decimal point 5 places to the right.
2.9 7 8 5 3
2.97853 × 105 = 297, 853
Express each number in standard notation.
1) 5.2564 × 109
=
2) 9.42 × 107
=
3) 3.6653 × 1013
=
4) 7.987 × 1015
=
5) 6.2 × 109
=
6) 2.5856 × 108
=
7) 4.002 × 1012
=
8) 1.25 × 1011
=
9) 9.5269 × 106
=
10) 3.415 × 1012
=
Muhammad Javed Iqbal
Page 9 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 6.10074 × 105 in standard notation.
Here the exponent is 5. We should move the decimal point 5 places to the right.
6.1 0 0 7 4
6.10074 × 105 = 610, 074
Express each number in standard notation.
1) 4.558 × 109
=
2) 8.48 × 106
=
3) 5.5 × 1012
=
4) 1.856 × 1014
=
5) 7.25 × 108
=
6) 6.4586 × 107
=
7) 1.589 × 1013
=
8) 9.1 × 1010
=
9) 4.0624 × 105
=
10) 8.65 × 1011
Muhammad Javed Iqbal
=
Page 10 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 0.0061 in scientific notation.
0.0 0 6 1
We should move the decimal point 3 places to the right. So, the exponent will be -3.
0.0061 = 6.1 × 10-3
Express each number in scientific notation.
1)
0.0736
=
2)
0.0092
=
3)
0.0005
=
4)
0.021
=
5)
0.00862 =
6) 0.000572 =
7)
0.026
=
8)
9)
0.152
=
10)
0.00589 =
11)
0.004526 =
12)
0.00067 =
13)
0.089
14)
0.18
=
Muhammad Javed Iqbal
Page 11 of 31
0.8599
=
=
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 0.000000743 in scientific notation.
We should move the decimal point 7 places to the right. So, the exponent will be -7.
0.0 0 0 0 0 0 7 4 3
0.000000743 = 7.43 × 10ˉ7
Express each number in scientific notation.
1) 0.0000000000034
=
2) 0.0000000408
=
3) 0.0000000000000092 =
4) 0.0000002726
=
5) 0.000000000000517 =
6) 0.0000045
=
7) 0.0000002149
=
8) 0.00000000623
=
9) 0.000000000000028 =
10) 0.000000001
Muhammad Javed Iqbal
=
Page 12 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 0.00000876 in scientific notation.
We should move the decimal point 6 places to the right. So, the exponent will be -6.
0.0 0 0 0 0 8 7 6
0.00000876 = 8.76 × 10ˉ6
Express each number in scientific notation.
1) 0.0000016
=
2) 0.000000008512
=
3) 0.0000000438
=
4) 0.000000000050
=
5) 0.00000079
=
6) 0.0000000006035
=
7) 0.000000000000391 =
8) 0.0000702
=
9) 0.0000004
=
10) 0.000000000000096 =
Muhammad Javed Iqbal
Page 13 of 31
javedmath.com
Name :
Score :
Scientific Notation
Express each number in scientific notation.
1)
0.0056
=
2)
24, 010
=
3) 4, 085
=
4)
0.017
=
5)
0.000796
=
6)
952
=
7)
50, 413
=
8)
0.004
=
=
Express each number in standard notation.
9)
2.445 × 103
=
10)
1.04 × 10ˉ4
11)
9.165 × 10ˉ2
=
12)
5.962 × 103 =
13)
2.2 × 10ˉ5
=
14)
3.12 × 10ˉ1
15)
8.0447 × 104
=
16)
1.278 × 102 =
Muhammad Javed Iqbal
Page 14 of 31
=
javedmath.com
Name :
Score :
Scientific Notation
Express each number in scientific notation.
1) 0.00000927
=
2) 85, 000, 000
=
3) 4, 202, 100
=
4) 0.000000000037
=
5) 1, 000, 000, 000
=
Express each number in standard notation.
6) 6.024 × 10ˉ13
=
7) 2.13 × 1011
=
8) 1.2 × 10ˉ8
=
9) 3.7 × 10ˉ9
=
10) 5.002 × 106
=
Muhammad Javed Iqbal
Page 15 of 31
javedmath.com
Name :
Score :
Scientific Notation
Express each number in scientific notation.
1) 0.0000000586
=
2) 256, 950, 000
=
3) 0.00000742
=
4) 586, 200
=
5) 0.0000000000091
=
Express each number in standard notation.
6) 3.175 × 1010
=
7) 4.1 × 10ˉ12
=
8) 2.03 × 10ˉ9
=
9) 9.196 × 107
=
10) 7.82 × 1010
=
Muhammad Javed Iqbal
Page 16 of 31
javedmath.com
Name :
Score :
Scientific Notation
Express each number in scientific notation.
1)
0.0045
=
2)
0.424
=
3)
0.069
=
4)
0.78126
=
5)
0.82
=
6)
0.57
=
7)
0.0004
=
8)
0.984
=
Express each number in standard notation.
9)
7.015 × 10ˉ1
11) 1.56 × 10ˉ2
=
=
10)
9.586 × 10ˉ4 =
12)
1.5 × 10ˉ3
=
13)
9.10 × 10ˉ3
=
14)
6.59 × 10ˉ1
=
15)
5.2 × 10ˉ2
=
16)
9.8 × 10ˉ3
=
Muhammad Javed Iqbal
Page 17 of 31
javedmath.com
Name :
Score :
Scientific Notation
Express each number in scientific notation.
1) 0.00000000479
=
2) 0.00009156
=
3) 0.0000000850
=
4) 0.00000000000594
=
5) 0.0000007
=
Express each number in standard notation.
6) 6.002 × 10ˉ10
=
7) 3.15 × 10ˉ13
=
8) 5.04 × 10ˉ9
=
9) 8.264 × 10ˉ7
=
10) 4.5 × 10ˉ12
Muhammad Javed Iqbal
=
Page 18 of 31
javedmath.com
Name :
Score :
Scientific Notation
Express each number in scientific notation.
1) 0.0000001046
=
2) 0.0000000000985
=
3) 0.00000860
=
4) 0.00004526
=
5) 0.0000000064
=
Express each number in standard notation.
6) 7.002 × 10ˉ9
=
7) 1.65 × 10ˉ12
=
8) 6.225 × 10ˉ10
=
9) 3.1 × 10ˉ8
=
10) 9.78 × 10ˉ11
=
Muhammad Javed Iqbal
Page 19 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 7.258 × 10ˉ5 in standard notation.
Here the exponent is –5. We should move the decimal point 5 places to the left.
0 0 0 0 0 7 . 2 5 8
7.258 × 10ˉ5 = 0.00007258
Express each number in standard notation.
1) 2.45 × 10ˉ12
=
2) 6.0012 × 10ˉ9
=
3) 1.256 × 10ˉ13
=
4) 5.9 × 10ˉ6
=
5) 4.013 × 10ˉ15
=
6) 8.3692 × 10ˉ9
=
7) 5.11 × 10ˉ13
=
8) 6.859 × 10ˉ5
=
9) 1.7425 × 10ˉ12
=
10) 9.52 × 10ˉ6
Muhammad Javed Iqbal
=
Page 20 of 31
javedmath.com
Name :
Score :
Scientific Notation
Example:
Write 4.5 × 10ˉ5 in standard notation.
Here the exponent is –5. We should move the decimal point 5 places to the left.
0 0 0 0 0 4 . 5
4.5 × 10ˉ5 = 0.000045
Express each number in standard notation.
1) 5.42 × 10ˉ10
=
2) 2.0016 × 10ˉ8
=
3) 6.521 × 10ˉ12
=
4) 9.5 × 10ˉ5
=
5) 3.014 × 10ˉ14
=
6) 2.9381 × 10ˉ8
=
7) 1.15 × 10ˉ10
=
8) 9.586 × 10ˉ6
=
9) 5.2471 × 10ˉ13
=
10) 2.59 × 10ˉ7
Muhammad Javed Iqbal
=
Page 21 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify and express in scientific notation:
Example 1
Example 2
(2 × 104) + (3 × 105)
(7 × 108) – (4 × 106)
= (2 × 104) + (3 × 104) × 10
= (7 × 106) × 102 – (4 × 106)
= (2 × 104) + (30 × 104)
= (700 × 106) – (4 × 106)
= 32 × 104
= 696 × 106
= 3.2 × 105
= 6.96 × 108
Simplify each problem and express the answer in scientific notation.
1) (2 × 103) + (5 × 105)
2) (4 × 108) – (9 × 107)
Answer :
Answer :
3) (8 × 109) – (3 × 107)
4) (5 × 107) + (1 × 106)
Answer :
Answer :
5) (4 × 102) + (7 × 103)
6) (9 × 105) – (6 × 104)
Answer :
Answer :
7) (1 × 106) – (8 × 104)
8) (5 × 109) + (3 × 108)
Answer :
Muhammad Javed Iqbal
Answer :
Page 22 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify and express in scientific notation:
Example 1
Example 2
(6 × 102) + (5 × 105)
(3 × 10ˉ3) – (2 × 10ˉ6)
= (6 × 102) + (5 × 102) × 103
= (3 × 10ˉ6) × 103 – (2 × 10ˉ6)
= (6 × 102) + (5000 × 102)
= (3000 × 10ˉ6) – (2 × 10ˉ6)
= 5006 × 102
= 2998 × 10ˉ6
= 5.006 × 105
= 2.998 × 10ˉ3
Simplify each problem and express the answer in scientific notation.
1) (3 × 10ˉ2) – (6 × 10ˉ5)
2) (8 × 103) + (5 × 10ˉ1)
Answer :
3) (7 × 107) + (4 × 104)
Answer :
4) (9 × 10ˉ5) – (6 × 10ˉ7)
Answer :
5) (5 × 106) – (8 × 103)
Answer :
6) (6 × 10ˉ7) + (7 × 10ˉ4)
Answer :
7) (3 × 10ˉ9) + (5 × 10ˉ5)
Answer :
8) (2 × 108) – (4 × 105)
Answer :
Muhammad Javed Iqbal
Answer :
Page 23 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify and express in scientific notation:
Example 1
Example 2
(1.2 × 102) + (3.04 × 105)
(5.54 × 10ˉ6) – (2.32 × 10ˉ8)
= (1.2 × 102) + (3.04 × 102) × 103
= (5.54 × 10ˉ8) × 102 – (2.32 × 10ˉ8)
= (1.2 × 102) + (3040 × 102)
= (554 × 10ˉ8) – (2.32 × 10ˉ8)
= 3041.2 × 102
= 551.68 × 10ˉ8
= 3.0412 × 105
= 5.5168 × 10ˉ6
Simplify each problem and express the answer in scientific notation.
1) (2.3 × 104) + (4.16 × 107)
2) (9.4 × 102) + (3.8 × 10ˉ1)
Answer :
3) (6.07 × 10ˉ1) – (4.52 × 10ˉ2)
Answer :
4) (7.98 × 107) – (1.24 × 105)
Answer :
5) (5.692 × 10ˉ4) + (8.8 × 10ˉ5)
Answer :
6) (4.6 × 102) – (2 × 10ˉ2)
Answer :
7) (9.18 × 109) – (3.9 × 106)
Answer :
8) (1.7 × 10ˉ1) + (6.504 × 102)
Answer :
Muhammad Javed Iqbal
Answer :
Page 24 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify and express in scientific notation:
Example 2
Example 1
(6 × 103) (2 × 105)
18 × 106
4 × 104
(6 × 103) (2 × 105) = 12 × 103 × 105
= 18 × 106 × 10ˉ4
4
=
= 12 × 108
4.5 × 102
= 1.2 × 109
Simplify each problem and express the answer in scientific notation.
1) (7 × 108) (9 × 106)
2) 3 × 104
8 × 10
Answer :
Answer :
3) 4 × 109
5× 107
4) (2 × 103) (3 × 104)
Answer :
5) (3 × 107) (9 × 106)
Answer :
6)
4 × 105
16 × 102
Answer :
7)
9 × 105
10 × 103
Answer :
8) (11 × 104) (7 × 102)
Answer :
Muhammad Javed Iqbal
Answer :
Page 25 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify and express in scientific notation:
Example 2
Example 1
(5 × 106) (7 × 109)
9 × 108
=
8 × 10ˉ2
(5 × 106) (7 × 109) = 35 × 106 × 109
= 35 × 1015
9
× 108 × 102
8
= 1.125 × 1010
= 3.5 × 1016
Simplify each problem and express the answer in scientific notation.
1) (2 × 107) (9 × 10ˉ3)
2) 15 × 10ˉ5
4 × 10ˉ7
Answer :
Answer :
3)
15 × 10ˉ7
16 × 10ˉ5
4) (9 × 108) (7 × 105)
Answer :
Answer :
5) (8 × 10ˉ7) (3 × 10ˉ6)
6)
Answer :
7) 4 × 108
1 × 104
Answer :
8) (4 × 103) (4 × 107)
Answer :
Muhammad Javed Iqbal
7 × 10ˉ3
16 × 102
Answer :
Page 26 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify and express in scientific notation:
Example 2
Example 1
2.5 × 106
=
0.5 × 103
2.5
× 106 × 10ˉ3
0.5
(3.5 × 104) (0.4 × 10ˉ7)
(3.5 × 104) (0.4 × 10ˉ7) = 1.4 × 104 × 10ˉ7
= 5 × 103
= 1.4 × 10ˉ3
Simplify each problem and express the answer in scientific notation.
1) 8.14 × 102
2 × 104
2) (0.6 × 103) (1.4 × 105)
Answer :
Answer :
3) 0.24 × 105
0.5 × 10ˉ7
4) (4.02 × 107) (0.9 × 10ˉ4)
Answer :
5) (3.7 × 10ˉ2) (6.4 × 10ˉ6)
Answer :
6) 5.10 × 109
0.6 × 10ˉ6
Answer :
7) 2.78 × 10ˉ3
0.8 × 10ˉ2
Answer :
8) (0.2 × 10) (7.2 × 105)
Answer :
Muhammad Javed Iqbal
Answer :
Page 27 of 31
javedmath.com
Name :
Score :
Scientific Notation
Express each number in scientific notation.
1)
0.0056
=
2)
24, 010
=
3) 4, 085
=
4)
0.017
=
5)
0.000796
=
6)
952
=
7)
50, 413
=
8)
0.004
=
=
Express each number in standard notation.
9)
2.445 × 103
=
10)
1.04 × 10ˉ4
11)
9.165 × 10ˉ2
=
12)
5.962 × 103 =
13)
2.2 × 10ˉ5
=
14)
3.12 × 10ˉ1
15)
8.0447 × 104
=
16)
1.278 × 102 =
Muhammad Javed Iqbal
Page 28 of 31
=
javedmath.com
Name :
Score :
Scientific Notation
Simplify each problem and express the answer in scientific notation.
1) (8 × 105) + (5 × 104)
Answer :
3) (3 × 104) – (5 × 102)
Answer :
5) 9 × 103
2 × 10
Answer :
7) (5 × 108) – (3 × 106)
Answer :
9) (4 × 102) + (9 × 104)
Answer :
Muhammad Javed Iqbal
2)
7 × 106
2 × 103
Answer :
4) (4 × 10) (2 × 103)
Answer :
6) (8 × 103) (3 × 104)
Answer :
8) (7 × 105) + (6 × 107)
Answer :
10) (2 × 103) (5 × 104)
Answer :
Page 29 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify each problem and express the answer in scientific notation.
1) (6 × 10ˉ5) + (2 × 10ˉ1)
2) (9 × 104) (5 × 107)
Answer :
Answer :
3)
8 × 10ˉ6
4 × 10ˉ2
4) (3 × 109) – (2 × 106)
Answer :
5) (9 × 102) – (3 × 10ˉ2)
Answer :
6) (7 × 104) + (6 × 107)
Answer :
7) (5 × 106) (4 × 109)
Answer :
9) (2 × 10ˉ6) + (7 × 10ˉ3)
Answer :
Muhammad Javed Iqbal
Answer :
8)
3 × 10ˉ7
8 × 10ˉ3
Answer :
10) (5 × 103) (5 × 10ˉ1)
Answer :
Page 30 of 31
javedmath.com
Name :
Score :
Scientific Notation
Simplify each problem and express the answer in scientific notation.
1) 3.2 × 104
1.6 × 102
2) (7.1 × 10ˉ2) + (5.02 × 10ˉ4)
Answer :
Answer :
3) (4.8 × 106) – (9.7 × 104)
4) (6.18 × 10ˉ1) (8.7 × 102)
Answer :
5) (5.98 × 10ˉ2) + (3.4 × 10ˉ4)
Answer :
6)
Answer :
7) (2.08 × 10ˉ7) (8.1 × 10ˉ5)
Answer :
9) (6.5 × 107) – (3.1 × 104)
Answer :
Muhammad Javed Iqbal
2.15 × 107
5 × 103
Answer :
8)
5.4 × 102
1.2 × 10ˉ1
Answer :
10) (1.98 × 10ˉ3) + (5.2 × 10ˉ6)
Answer :
Page 31 of 31
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