﻿ Scientific Notation Worksheets - Page 13 | Problems & Solutions

# Scientific Notation Worksheets - Page 13

Scientific Notation Worksheets
• Page 13
121.
Identify 5.849 × 106 in standard form.
 a. 5849 b. 584900 c. 58490 d. 5849000

#### Solution:

As the exponent of 10 in the number is 6, move the decimal point 6 places to the right.

5.849 × 106 = 5849000
[As there are only 3 digits after the decimal, insert 3 zeroes at the end.]

122.
Write 5.4 × 10-5 in standard form.
 a. 0.00054 b. 5.4e-05 c. 0.0054 d. 54000

#### Solution:

5.4 x 10-5 = 0.000054
[Since the exponent of 10 is -5, move decimal point 5 places to left.]

So, the standard form of 5.4 x 10-5 is 0.000054.

123.
Express 80000000 in scientific notation.
 a. 8 × 108 b. 8 × 107 c. 8 d. 8 × 106

#### Solution:

A number is expressed in scientific notation as a product of two factors. The first one is a number between 1 and 10 and the second factor is an exponent of 10.

The first factor is 8.
[Move the decimal point 7 places to the left to get a number between 0 and 10.]

The second factor is 107.
[As the decimal is moved 7 places to the right, take 7 as exponent of 10.]

So, 80000000 can be written in scientific notation as 8 × 107.

124.
Solve the expression (7.3 × 103) (4.3 × 104) and express the result in scientific notation.
 a. 3.139 x 106 b. 3.139 c. 3.139 x 107 d. 3.139 x 108

#### Solution:

(7.3 x 103) (4.3 x 104) = (7.3 x 4.3) (103 x 104)
[Use multiplication properties.]

= 31.39 x 107
[Use product of powers property.]

= (3.139 x 101) x 107
[Write 31.39 in scientific notation.]

= 3.139 x 108
[Use product of powers property.]

125.
Solve (5.9 × 107) (6.5 × 10-5) and write the result in scientific notation.
 a. 3.835 b. 3.835 x 103 c. 3.835 x 10-3 d. 3.835 x 102

#### Solution:

(5.9 x 107) (6.5 x 10-5) = (5.9 x 6.5) (107 x 10-5)
[Use multiplication properties.]

= (38.35) (102)
[Use product of powers property.]

= (3.835 x 101) x 102
[Write 38.35 in scientific notation.]

= 3.835 x 103
[Use product of powers property.]

126.
Simplify (0.34 × 104) / (3.4 × 10-4) and write the result in scientific notation.
 a. 1.0 x 108 b. 1.0 x 10-7 c. -1.0 x 107 d. 1.0 x 107

#### Solution:

(0.34 x 104) / (3.4 x 10-4) = (0.34 / 3.4) x (104 / 10-4)
[Write as a product.]

= 0.1 x (108)
[Use quotient of powers property.]

= (1.0 x 10-1) x 108
[Write 0.1 in scientific notation.]

= 1.0 x 107
[Use product of powers property.]

127.
Simplify (2.0 × 10-13) / (10 × 10-9) and write the result in scientific notation.
 a. 2 x 105 b. -2 x 105 c. 2 x 10-5 d. -2 x 10-5

#### Solution:

(2.0 x 10-13) / (10 x 10-9) = (2.0 / 10) x (10-13 / 10-9)
[Write as a product.]

= 0.2 x 10-4
[Use quotient of powers property.]

= (2 x 10-1) x 10-4
[Write 0.2 in scientific notation.]

= 2 x 10-5
[Use product of powers property.]

128.
Simplify:
(7 × 10-7)2
 a. 4.9 × 1013 b. - 4.9 × 1013 c. 4.9 × 10- 13 d. - 4.9 × 10- 13

#### Solution:

(7 × 10-7)2 = 72 × (10-7)2
[Use power of a product property.]

= 49 × 10-14
[Use power of a power property.]

= (4.9 × 101) × 10-14
[Write 49 in scientific notation.]

= 4.9 × 10-13
[Use product of powers property.]

129.
Write 83972 in scientific notation.
 a. 839.72 x 1016 b. 83.972 x 104 c. 83.972 d. 8.3972 x 104

#### Solution:

A number is expressed in scientific notation as a product of two factors. The first factor is a number between 1 and 10 and the second factor is an exponent of 10.

The first factor is 8.3972.
[Move the decimal point such that the number is between 1 and 10.]

The second factor is 104.
[As the decimal is moved 4 places to the left, take the exponent of 10 as 4.]

So, the number 83972 in scientific notation is 8.3972 x 104.

130.
A teacher asked four students to evaluate 5 × 104. Sunny answered 5000, Jeff answered 50000, Andy answered 500000, and William answered 5000000. Who among the four was correct?
 a. Andy b. William c. Jeff d. Sunny

#### Solution:

5 x 104 = 5 x 10000
[Evaluate power.]

= 50000
[Multiply 5 and 10000.]

So, Jeff is correct.