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 10x) (M X 10y) = (N) (M) X 10x+y

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

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

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) =

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

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) =

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

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

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

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

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 =

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

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 =

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

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