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: 15. 97 X 1014 Shift Decimal left one place. Final Answer: 1. 597 X 1014
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. 319 X 10 -7 Shift decimal left one place. Final Answer: 2. 43 X 10 -6
Practice Worksheet Practice Multiplying in Scientific Notation (2. 4 X 10 -3)(4. 5 X 10 -3) = (5. 67 X 10^3)(3. 9 X 10^-6) = (4. 78 X 107)(9. 3 X 10 -2) = (8. 9 X 10^-2)(6. 5 X 10^4) = (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. 08 X 10 -5 (5. 67 X 10^3)(3. 9 X 10^-6) = 2. 21 X 10^-2 (4. 78 X 107)(9. 3 X 10 -2) = 4. 45 X 106 (8. 9 X 10^-2)(6. 5 X 10^4) = 5. 785 X 10^3 (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 10^4)(9. 1 X 10^2) = (2. 0 X 10 -3)(2. 3 X 104) = (7. 4 X 10^2)(6. 5 X 10^7) = (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. 584 X 10 -14 (5. 1 X 10^4)(9. 1 X 10^2) = 4. 641 X 10^7 (2. 0 X 10 -3)(2. 3 X 104) = 4. 6 X 101 (7. 4 X 10^2)(6. 5 X 10^7) = 4. 81 X 10^10 (9. 4 X 10 -5)(3. 1 X 105) = 2. 914 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. 81 Subtract exponents: (2)-(-5)=7 Answer: 2. 81 X 107
Practice Worksheet Practice Dividing in Scientific Notation 3. 0 X 104 / 1. 5 X 10 -2 = 4. 5 X 10^2 / 2. 4 X 10^-5 = 4. 9 X 105 / 1. 45 X 108 = 6 X 10^5 / 3 X 10^-7 = 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 10^2 / 2. 4 X 10^-5 = 1. 875 X 10^7 4. 9 X 105 / 1. 45 X 108 = 3. 37 X 10 -3 6 X 10^5 / 3 X 10^-7 = 2 X 10^12 2. 46 X 106 / 4. 523 X 103 = 5. 44 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 10^-5 / 4 X 10^3 = 4 X 10^2 / 2 X 10^-8 = 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. 13 X 108 3. 45 X 108 / 2. 6 X 103 = 1. 33 X 105 8. 21 X 10^-5 / 4 X 10^3 = 2. 1 X 10^-8 4 X 10^2 / 2 X 10^-8 = 2 X 10^10 3. 4 X 10 -8 / 1. 2 X 10 -4 = 2. 83 X 10 -4
Links for more information and practice • Math Skills • http: //janus. astro. umd. edu/astro/scinote /
- Slides: 16