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Multiplying and Dividing in Scientific Notation

Multiplying and Dividing in Scientific Notation. Multiplying Numbers in Scientific Notation. Multiply the base numbers together. Then add the exponents to get the power of 10. General formula : (N X 10 x ) (M X 10 y ) = (N) (M) X 10 x+y. Example 1. Given: (3.42 X 10 5 )(4.67 X 10 9 )

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Multiplying and Dividing in Scientific Notation

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  1. Multiplying and Dividing in Scientific Notation

  2. Multiplying Numbers in Scientific Notation • Multiply the base numbers together. • Then add the exponents to get the power of 10. • General formula: (N X 10x) (M X 10y) = (N) (M) X 10x+y

  3. Example 1 • Given: (3.42 X 105)(4.67 X 109) • Multiply bases: 3.42 X 4.67 = 15.97 • Add Exponents: 105 · 109=105+9=1014 • Answer: 16.0 X 1014 • Shift Decimal left one place. • Final Answer: 1.6 X 1015

  4. Example 2 • Given: (2.93 X 10-2)(8.3 X 10-5) • Multiply Bases: 2.93 X 8.3 = 24.319 • Add Exponents: 10-2· 10-5=10-2+(-5)=10-7 • Answer: 24.3 X 10-7 • Shift decimal left one place. • Final Answer: 2.4 X 10-6

  5. Practice Worksheet Practice Multiplying in Scientific Notation (2.4 X 10-3)(4.5 X 10-3) = (5.67 X 10³)(3.9 X 10ˉ⁶) = (4.78 X 107)(9.3 X 10-2) = (8.9 X 10ˉ²)(6.5 X 10⁴) = (3.4 X 108)(5 X 103) =

  6. Practice Worksheet Practice Multiplying in Scientific Notation (2.4 X 10-3)(4.5 X 10-3) = 1.1 X 10-5 (5.67 X 10³)(3.9 X 10ˉ) = 2.2 X 10ˉ² (4.78 X 107)(9.3 X 10-2) = 4.5 X 106 (8.9 X 10ˉ²)(6.5 X 10⁴) = 5.8 X 10³ (3.4 X 108)(5 X 103) = 1.7 X 1012

  7. Practice Worksheet Practice Multiplying in Scientific Notation (1.6 X 10-6)(9.9 X 10-9) = (5.1 X 10⁴)(9.1 X 10²) = (2.0 X 10-3)(2.3 X 104) = (7.4 X 10²)(6.5 X 10⁷) = (9.4 X 10-5)(3.1 X 105) =

  8. Practice Worksheet Practice Multiplying in Scientific Notation (1.6 X 10-6)(9.9 X 10-9) = 1.6 X 10-14 (5.1 X 10⁴)(9.1 X 10²) = 4.6 X 10⁷ (2.0 X 10-3)(2.3 X 104) = 4.6 X 101 (7.4 X 10²)(6.5 X 10⁷) = 4.8 X 10¹⁰ (9.4 X 10-5)(3.1 X 105) = 2.9 X 101

  9. Dividing Numbers in Scientific Notation • Divide the base numbers. • Then subtract the exponents to get the power of 10. • General formula: N X 10x / M X 10y = N/M X 10x-y

  10. Example 1 • Given: 8 X 10-3 2 X 10-2 • Divide bases: 8/2=4 • Subtract exponents: (-3)-(-2)=-1 • Answer: 4 X 10-1

  11. Example 2 • Given: 3.45 X 102 1.23 X 10-5 • Divide bases: 3.45/1.23= 2.80487… • Subtract exponents: (2)-(-5)=7 • Answer: 2.8 X 107

  12. Practice Worksheet Practice Dividing in Scientific Notation 3.0 X 104 / 1.5 X 10-2 = 4.5 X 10² / 2.4 X 10ˉ⁵ = 4.9 X 105 / 1.45 X 108 = 6 X 10⁵ / 3 X 10ˉ⁷ = 2.46 X 106 / 4.523 X 103 =

  13. Practice Worksheet Practice Dividing in Scientific Notation 3.0 X 104 / 1.5 X 10-2 = 2.0 X 106 4.5 X 10² / 2.4 X 10ˉ⁵ = 1.9 X 10⁷ 4.9 X 105 / 1.45 X 108 = 3.4 X 10-3 6 X 10⁵ / 3 X 10ˉ⁷ = 2 X 10¹² 2.46 X 106 / 4.523 X 103 = 5.4 X 102

  14. Practice Worksheet Practice Dividing in Scientific Notation 1.51 X 105 / 3.66 X 10-4 = 3.45 X 108 / 2.6 X 103 = 8.21 X 10ˉ⁵ / 4 X 10³ = 4 X 10² / 2 X 10ˉ⁸ = 3.4 X 10-8 / 1.2 X 10-4 =

  15. Practice Worksheet Practice Dividing in Scientific Notation 1.51 X 105 / 3.66 X 10-4 = 4.1 X 108 3.45 X 108 / 2.6 X 103 = 1.3 X 105 8.21 X 10ˉ⁵ / 4 X 10ˉ³ = 2.1 X 10ˉ⁸ 4 X 10² / 2 X 10ˉ⁸ = 2.0 X 10¹⁰ 3.4 X 10-8 / 1.2 X 10-4 = 2.8 X 10-4

  16. Links for more information and practice • Math Skills • http://janus.astro.umd.edu/astro/scinote/

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