Multiplying and Dividing in Scientific Notation Multiplying Numbers
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 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 10 x / M X 10 y = N/M X 10 x-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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