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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 10xy

Example 1

- Given (3.42 X 105)(4.67 X 109)
- Multiply bases 3.42 X 4.67 15.97
- Add Exponents 10510910591014
- 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 10-210-510-2(-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 103)(3.9 X 10-6) (4.78 X

107)(9.3 X 10-2) (8.9 X 10-2)(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)

1.08 X 10-5 (5.67 X 103)(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 104) 5.785 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)

1.584 X 10-14 (5.1 X 104)(9.1 X 102) 4.641

X 107 (2.0 X 10-3)(2.3 X 104) 4.6 X

101 (7.4 X 102)(6.5 X 107) 4.81 X

1010 (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 10x / M X 10y N/M X 10x-y

Example 1

- Given8 X 10-3 / 2 X 10-2
- Divide bases 8/24
- Subtract exponents (-3)-(-2)-1
- Answer 4 X 10-1

Example 2

- Given3.45 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 102 / 2.4 X 10-5 4.9 X 105 / 1.45 X

108 6 X 105 / 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 102 / 2.4 X 10-5 1.875 X

107 4.9 X 105 / 1.45 X 108 3.37 X 10-3 6 X

105 / 3 X 10-7 2 X 1012 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

103 4 X 102 / 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 103 2.1 X 10-8 4 X

102 / 2 X 10-8 2 X 1010 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/

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