Multiplying and Dividing

in Scientific Notation

8th Grade

Multiplying Numbers in

Scientific Notation

Multiplying with scientific notation requires at least three

(and sometimes four) steps.

1. Multiply the coefficients

2. Multiply the powers of ten

3. Combine those results

4. Put in proper form

6.0 x 2.5 = 15

104

x 102

= 106

15 x 106

1.5 x 107

1. Multiply the coefficients

2. Multiply the powers of ten

3. Combine those results

4. Put in proper form

Evaluate: (6.0 x 104)(2.5 x 10

2)

Multiplying Numbers in Scientific Notation

Multiplying Numbers in Scientific Notation

• Multiply the decimal numbers together.

• 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 decimals: 3.42 X 4.67 = 15.97

• Add Exponents: 105 x 109=105+9=1014

• Preliminary Answer: 15.97 X 1014

• Now, Rewrite in Scientific Notation if needed.

• Final Answer:

1.597 X 1015

Example 2

• Given: (2.93 X 10-2) • (8.3 X 10-5)

• Multiply Decimals: 2.93 X 8.3 = 24.319

• Add Exponents: 10-2 x 10-5=10-2+(-5)=10-7

• Answer: 24.319 X 10-7

• Rewrite in Scientific Notation

• Final Answer: 2.43 X 10-6

1. Multiply the coefficients

2. Multiply the powers of ten

3. Combine those results

4. Put in proper form

Evaluate: (4.80 x 106)(9.0 x 10

-8)

Multiplying Numbers in Scientific Notation

35 Evaluate (2.0 x 10-4

)(4.0 x 107). Express

the result in scientific notation.

A 8.0 x 1011

B 8.0 x 103

C 5.0 x 103

D 5.0 x 1011

E 7.68 x 10-28

F 7.68 x 10-28

36 Evaluate (5.0 x 106)(7.0 x 10

7)

A 3.5 x 1013

B 3.5 x 1014

C 3.5 x 101

D 3.5 x 10-1

E 7.1 x 1013

F 7.1 x 101

37 Evaluate (6.0 x 102)(2.0 x 10

3)

A 1.2 x 106

B 1.2 x 101

C 1.2 x 105

D 3.0 x 10-1

E 3.0 x 105

F 3.0 x 101

38 Evaluate (1.2 x 10-6

)(2.5 x 103). Express the result in

scientific notation.

A 3 x 103

B 3 x 10-3

C 30 x 10-3

D 0.3 x 10-18

E 30 x 1018

39 Evaluate (1.1 x 104)(3.4 x 10

6). Express the result in

scientific notation.

A 3.74 x 1024

B 3.74 x 1010

C 4.5 x 1024

D 4.5 x 1010

E 37.4 x 1024

40 Evaluate (3.3 x 104)(9.6 x 10

3). Express the result in

scientific notation.

A 31.68 x 107

B 3.168 x 108

C 3.2 x 107

D 32 x 108

E 30 x 107

41 Evaluate (2.2 x 10-5

)(4.6 x 10-4

). Express the result in

scientific notation.

A 10.12 x 10-20

B 10.12 x 10-9

C 1.012 x 10-10

D 1.012 x 10-9

E 1.012 x 10-8

Dividing Numbers in Scientific Notation

Dividing with scientific notation follows the same basic rules

as multiplying.

1. Divide the coefficients

2. Divide the powers of ten

3. Combine those results

4. Put in proper form

Dividing Numbers in Scientific Notation

• Divide the decimal numbers.

• Then subtract the exponents

• General formula:

1010

10

xx y

y

N N

MM

Division with Scientific Notation

5.4 ÷ 9.0 = 0.6

106÷ 10

2= 10

4

0.6 x 104

6.0 x 103

1. Divide the coefficients

2. Divide the powers of ten

3. Combine those results

4. Put in proper form

Evaluate: 9.0 x 10

2

5.4 x 106

Example 1

• Given: 8 • 10-3

2 • 10-2

• Divide decimals: 8÷2 = 4

• Subtract exponents: (-3)-(-2)= -1

• Final Answer: 4 •10-1

Example 2

• Given: 3.45 X 102

1.23 X 10-5

• Divide decimals: 3.45 ÷ 1.23= 2.81

• Subtract exponents: 2- -5 =7

• Answer: 2.81 X 107

Division with Scientific Notation

1. Divide the coefficients

2. Divide the powers of ten

3. Combine those results

4. Put in proper form

Evaluate:

1.1 x 10-3

4.4 x 106

42 Evaluate 4.16 x 10-9

5.2 x 10-5

Express the result in scientific notation.

A 0.8 x 10-4

B 0.8 x 10-14

C 0.8 x 10-5

D 8 x 10-4

E 8 x 10-5

43 Evaluate 7.6 x 10-2

4 x 10-4

Express the result in scientific notation.

A 1.9 x 10-2

B 1.9 x 10-6

C 1.9 x 102

D 1.9 x 10-8

E 1.9 x 108

44 Evaluate 8.2 x 103

2 x 107

Express the result in scientific notation.

A 4.1 x 10-10

B 4.1 x 104

C 4.1 x 10-4

D 4.1 x 1021

E 4.1 x 1010

45 Evaluate 3.2 x 10-2

6.4 x 10-4

Express the result in scientific notation.

A .5 x 10-6

B .5 x 10-2

C .5 x 102

D 5 x 101

E 5 x 103

46 The point on a pin has a diameter of approximately

1 x 10-4

meters. If an atom has a diameter of

2 x 10-10

meters, about how many atoms could fit

across the diameter of the point of a pin?

A 50,000

B 500,000

C 2,000,000

D 5,000,000

Question from ADP Algebra I

End-of-Course Practice Test

Question 1 Write these 2 numbers in scientific notation:

0.000467 32000000

Question 2 Express 5.43 x 10-3 in standard form

Question 3 (4.5 x 10-14) x (5.2 x 103) = ?

Question 4 (6.1 x 105)/(1.2 x 10-3) = ?

Question 5 (3.74 x 10-3)4 = ?

Practice Quiz Questions

Homework

• IXL due Friday

– Must get to a smart score of 90 or better; should get to smart score of 100

• A.8

• A.9

• A.10

• W.1

• W.2

• W.3

• W.4