Solutions to Problems on Scientific Notation

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Section A: The Definition of the Notation (Decimal => Scientific)


Write the follwing numbers in scientific notation.

1. 1001 = 1.001x103 6. 0.13592 = 1.3592x10-1
2. 53 = 5.3x101 7. -0.0038 = -3.8x10-3
3. 6,926,300,000 = 6.9263x109 8. 0.00000013 = 1.3x10-7
4. -392 = -3.92x102 9. -0.567 = -5.67x10-1
5. 0.00361 = 3.61x10-3  



Section B: Converting Back (Scientific => Decimal)

1. 1.92 x 103 = 1,920 6. 1.03 x 10-2 = 0.0103
2. 3.051x101 = 30.51 7. 8.862 x 10-1 = 0.8862
3. -4.29 x 102 = -429 8. 9.512 x 10-8 = 0.00000009512
4. 6.251 x 109 = 6,251,000,000 9. -6.5 x 10-3 = -0.0065
5. 8.317 x 106 = 8,317,000 10. 3.159 x 102 = 315.9



Section C: Multiplication, Division and ... with Scientific Notation


Use Scientific Notation (and only the scientific notation!) to find the answer to the following multiplictions, divisions, additions.

1. 4.1357 x 10-15 * 5.4 x 102 = 2.2 x 10-12
2. 1.695 x 104 ÷ 1.395 x 1015 = 1.215 x 10-11
3. 4.367 x 105 * 1.96 x 1011 = 8.56 x 1016
4. 6.97 x 103 * 2.34 x 10-6 + 3.2 x 10-2 = 4.83 x 10-2
5. 5.16 x 10-4 ÷ 8.65 x 10-8 + 9.68 x 104 = 1.03 x 105


Section D: Significant Figures

For the following, write each with the correct number of significant figures.

1. 2.38617954 x 10-1 * 1.15197705 x 106 = 2.7488240 x 105
 2. 3.0001 * 5 = 15.001
3. 1.12 x 105 * 6.06 x 105 = 6.79 x 1010
4. 2.27513 x 103 * 1.9376 x 102 = 4.4083 x 105
5. 2 x 101 * 3.0 x 101 = 6.0 x 102
6. 5.567 x 108 / 2.215 x 108 = 2.513 x 100
7. 2.775 x 10-4 * 4.775 x 104 = 1.325 x 101
8. 5 / 8.14 x 102 = 6.14 x 10-3
9. 4.7192 x 102 / 3.862 x 10-4 = 1.222 x 106


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