# Scientific Notation Worksheets - Page 14

Scientific Notation Worksheets
• Page 14
131.
A hydrogen atom has a mass of 1.67 × 10-27 kilogram. Express the mass of 4 × 102 hydrogen atoms in scientific notation.
 a. 6.68 x 10-25 kilogram b. 6.68 x 1029 kilogram c. 6.68 x 10-29 kilogram d. 6.68 x 1025 kilogram

#### Solution:

The mass of a hydrogen atom is 1.67 x 10-27 kilogram.

The mass of 4 x 102 hydrogen atoms is (1.67 x 10-27 ) x (4 x 102)

= (1.67 x 4) x (10-27 x 102) kilogram
[Use commutative property of multiplication.]

= 6.68 x (10-27 x 102) kilogram
[Multiply 1.67 and 4.]

= 6.68 x 10-25 kilogram

132.
The weight of an elephant is 1600 kgs. Write the number in scientific notation.
 a. 1.6 x 103 b. 16 x 10-3 c. 1.6 d. 1.6 x 104

#### Solution:

A number is expressed in scientific notation as the 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 1.6.
[Move the decimal point such that the number is greater than 1 but less than 10.]

The second factor is 103.
[As the decimal is moved 3 places to the left, take the exponent of 10 as 3.]

So, the number 1600 in scientific notation is 1.6 x 103.

133.
Order the numbers 130 × 102, 16.3 × 105, 0.061 × 104 from the greatest to the least.
 a. 130 x 102 > 16.3 x 105 > 0.061 x 104 b. 0.061 x 104 > 16.3 x 105 > 130 x 102 c. 16.3 x 105 > 130 x 102 > 0.061 x 104 d. None of the above

#### Solution:

130 x 102 = 1.30 x 102 x 102
[Write 130 as 1.30 x 102.]

= 1.30 x 104

= 13000
[Simplify.]

16.3 x 105 = 1.63 x 101 x 105
[Write 16.3 as 1.63 x 101.]

= 1.63 x 106

= 1630000
[Simplify.]

0.061 x 104 = 6.100 x 10-2 x 104
[Write 0.061 as 6.100 x 10-2.]

= 6.100 x 102

= 610
[Simplify.]

Since 1630000 > 13000 > 610, the order is 16.3 x 105 > 130 x 102 > 0.061 x 104.

134.
In _______ notation, we change expressions from scientific notation by simplifying the product of two factors.
 a. Exponential b. Standard c. Scientific d. Algebric

#### Solution:

We change expressions from scientific notation to standard notation by simplifying the product of two factors.

135.
Multiply 5 × 106 and 6 × 10-3. Express the result in scientific notation.
 a. 3 b. 3 x 103 c. 3 x 104 d. 30

#### Solution:

= 5 x 6 x 106 x 10-3
(5 x 106 ) x (6 x 10-3 )
[Use commutative property of multiplication.]

= 30 x 106 x 10-3
[Multiply 5 and 6.]

= 30 x 103

= 3 x 101 x 103
[Write 30 = 3 x 101 in scientific notation.]

= 3 x 104

136.
Find the values of $a$ and $b$ in the table.
 3 x 101 3 x 10 30 3 x 100 3 x 1 3 3 x 10-2 3 x $a$ $b$
 a. 0.01, 0.03 b. 1.00, 3.00 c. 0.10, 0.30 d. None of the above

#### Solution:

3 x 10-2 = 3 x 1/102
[Write as a positive exponent.]

= 3 x 1100 = 3 x 0.01

= 0.03

The value of a is 0.01 and the value of b is 0.03.

137.
Find the values of $a$ and $b$ in the table.
 2 x 102 2 x 100 200 2 x 100 2 x $a$ $b$
 a. $a$ = 2, $b$ = 1 b. $a$ = 1, $b$ = 2 c. $a$ = 1, $b$ = 3 d. $a$ = 2, $b$ = 3

#### Solution:

2 x 100 = 2 x 1 = 2

The value of a is 1 and b is 2.

138.
Write 29000 in scientific notation.
 a. 2.9 × 105 b. 2.9 × 103 c. 2.9 × 104 d. None of the above

#### Solution:

A number in scientific notation is represented 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 in the scientific notation of 29000 is 2.9.
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 104.
[The decimal point is moved 4 places to the left. Use this number as the exponent of 10.]

So, the scientific notation of 29000 is 2.9 × 104.

139.
Write 310000000 in scientific notation.
 a. 3.1 × 108 b. 3.1 × 109 c. 3.1 × 107 d. 3.1 × 106

#### Solution:

A number in scientific notation is 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 in the scientific notation of 310000000 is 3.1.
[Move the decimal point to get a factor greater than 1 and less than 10.]

The second factor is 108 .
[The decimal point moved 8 places to the left. Use this number as the exponent of 10.]

So, the scientific notation of 310000000 is 3.1 × 108.

140.
The speed of sound in air is 331 m/s at 0oC. Write the speed of sound in air in scientific notation.
 a. 3.31 x 101 b. 3.31 x 103 c. 3.31 x 102 d. None of the above

#### Solution:

A number in scientific notation is 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 in the scientific notation of 331 is 3.31
[Move the decimal point to get a factor greater than or equal to 1 and less than 10.]

The second factor is 102
[The decimal point is moved 2 places to the left. Use this number as the exponent of 10.]

The speed of sound in air in scientific notation is 3.31 x 102 m/s.