# Scientific Notation Worksheets - Page 9

Scientific Notation Worksheets
• Page 9
81.
The Orbital Eccentricity of the Venus is about 6.8 × 10-3. Choose the standard form.
 a. 0.068 b. 0.00068 c. 0.0068 d. 0.68

#### Solution:

6.8 × 10-3 = 0.0068
[Multiplying by 0.001 moves the decimal point 3 places to the left.]

The Orbital Eccentricity of the Venus expressed in standard form is 0.0068.

82.
The diameter of a proton is about 1 × 10-12 mm. Identify the standard form.
 a. 1e-12 b. 1.2e+10 c. 1e+11 d. 1e+07

#### Solution:

1 × 10-12 = 0.000000000001
[Multiplying by 0.000000000001 moves the decimal point 12 places to the left.]

The diameter of a proton expressed in standard form is 0.000000000001 mm.

83.
The lowest temperature in a lab setting is about 2.8 × 10-10 °k. Identify the number in standard form.
 a. 2.8e-10 b. 2.8e-11 c. 2.8e-09 d. 2.8e-08

#### Solution:

2.8 × 10-10 = 0.00000000028
[Multiplying by 0.0000000001 moves the decimal point 10 places to the left.]

The lowest temperature in a lab setting expressed in standard form is 0.00000000028 °k.

84.
Identify 7.8 × 10- 3 in standard form.
 a. 7.8 b. 0.78 c. 0.078 d. 0.0078

#### Solution:

7.8 × 10-3 = 007.8 × 10-3
[Since exponent is negative 7.8 × 10-3 is a small number. Shift the decimal point 3 places to the left.]

= 0.0078

The standard form of 7.8 × 10-3 is 0.0078.

85.
What is the value of $n$, if 6980 = 6.98 × 10$n$?
 a. 3 b. 4 c. 2 d. 5

#### Solution:

Write 6980 in scientific notation.

6980 = 6.98 × 103
[Shift the decimal point 3 places to left to get a number greater than or equal to 1 and less than 10 and use 3 as an exponent of 10.]

6980 = 6.98 × 10n

6.98 × 103 = 6.98 × 10n
[Substitute 6980 = 6.98 × 103.]

Since the two factors are equal, the exponents of 10 are equal.

The value of n is 3.

86.
Which of the numbers is greater, 6 × 102 or 7 × 103?
 a. 6 x 102 b. 7 x 103 c. Both are same d. None of the above

#### Solution:

Since 3 > 2, 103 > 102
[Order the exponents of two numbers.]

7 x 103 > 6 x 102
[Compare the two numbers and order from greatest to least.]

The number 7 x 103 is greater.

87.
An alloy of bronze used for making bush bearing contains 8% graphite. Express your answer using scientific notation.
 a. 8 x 10-2 b. 8 x 10-3 c. 8 x 10-4 d. 8 x 10-1

#### Solution:

8% = 8100= 0.08
[Write in decimal form.]

0.08 = 8 x 0.01
[Shift the decimal point 2 places to right to get a number greater than or equal to 1 and less than 10.]

= 8 x 10-2
[0.01 = 1 / 100= 10-2.]

The scientific notation of 8% is 8 x 10-2.

88.
Write the scientific notation of the fraction $\frac{4}{4000}$.
 a. 1 x 10-1 b. 1 x 10-4 c. 1 x 10-3 d. 1 x 10-2

#### Solution:

44000 = 11000
[Simplify.]

= 0.001
[Write in decimal form.]

= 1 x 0.001
[Shift the decimal point 3 places to right to get a number greater than or equal to 1 and less than 10.]

= 1 x 10-3
[0.001 = 1 / 1000= 10-3.]

The scientific notation of the fraction is 1 x 10-3.

89.
Express 670,000,000,000 in scientific notation.
 a. 67 × 1010 b. 6.7 × 1010 c. 0.67 × 1011 d. 6.7 × 1011