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 =
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: X 102
1.23 X 10-5
Divide bases: 3.45/1.23= …
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 / 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 / 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