﻿ Fractions and Decimals Worksheets - Page 10 | Problems & Solutions Fractions and Decimals Worksheets - Page 10

Fractions and Decimals Worksheets
• Page 10
91.
Express the decimal number 0.81818181... as a fraction. a. $\frac{9}{11}$ b. $\frac{41}{50}$ c. $\frac{40}{49}$ d. None of the above

Solution:

Let the variable N equal the decimal.

N = 0.81818181...

100N = 81.81818181...
[Multiply each side by 102, or 100, because 2 digits repeat.]

100N = 81.81818181...
N =   0.81818181...
-----------------------------
99N = 81.000000...
-----------------------------

[Subtract to eliminate the repeating decimal.]

99N = 81

N = 8199
[Divide each side by 99.]

N = 911
[Divide the numerator and the denominator by their G.C.F.]

92.
In the practice session, Steven ran 21.218 miles in 2 hours and 17.365 miles in another 1 hour 30 minutes. About how many miles did he run in all? a. 15 b. 50 c. 38 d. 20

93.
Find the decimal number that is equivalent to the fraction of 15 minutes in an hour. a. 0.40 b. 0.25 c. 0.28 d. None of the above

Solution:

The fraction of 15 minutes in an hour = 15 / (the number of minutes in one hour).

1560
[Substitute the values..]

= 14
[Divide the numerator and the denominator by their G.C.F.]

= 0.25
[Convert the fraction to a decimal number.]

94.
Which of the following fractions is a terminating decimal?
(I) $\frac{4}{9}$
(II) $\frac{5}{4}$
(III) $\frac{8}{11}$ a. Both (I) and (III) b. Both (II) and (III) c. Only (II) d. Only (I)

Solution:

A fraction can be converted into a decimal by dividing the numerator by the denominator. If the division ends with a remainder of zero, the decimal is called a terminating decimal.

Consider the first fraction, 4 / 9 :
4 / 9 = 0.44444444...
[Convert the fraction into a decimal number.]

Consider the second fraction, 5 / 4 :
5 / 4 = 1.25
[Convert the fraction into a decimal number.]

Consider the third fraction, 8 / 11:
8 / 11= 0.72727272...
[Convert the fraction into a decimal number.]

Among the fractions, the second fraction is a terminating decimal.

95.
Company1 buys 75 shares from Company2 having a total of 100 shares. Which of the following decimal numbers is equivalent to the fraction of shares left with Company2 to the total number of shares that were owned by Company2? a. 0.50 b. 0.30 c. 0.25 d. None of the above

Solution:

The fraction that represents the number of shares left with Company2 to the total number of shares which were owned by Company2 = (the total number of shares that were owned by Company2 - the number of shares that Company1 bought from Company2) / (the total number of shares that were owned by Company2).

= 100-75100
[Substitute the values.]

= 25100
[Subtract the numerator.]

= 14
[Divide the numerator and the denominator by their G.C.F.]

= 0.25
[Convert the fraction into a decimal number.]

Among the choices, the decimal number 0.25 equivalent to the fraction that represents the number of shares left with Company2 to the total number of shares that were owned by Company2.

96.
Which of the following decimals equals the fraction representing one piece in an eight-piece pizza? a. 0.5 b. 0.4 c. 0.125 d. None of the above

Solution:

The fraction representing one piece in an eight-piece pizza = 1 / 8 .

= 0.125
[Convert the fraction to a decimal number.]

Among the choices, the decimal that equals the fraction representing one piece in an eight-piece pizza is 0.125.

97.
Write the decimal, which represents the fraction of the alphabet A from the pie diagram.  a. 0.03 b. 0.333333........ c. 3.3 d. None of tha above

Solution:

The alphabet A has a value = 120.

The total value of the circle is 360.

The fraction that represents alphabet A is 120 / 360 = 1 / 3 .

= 0.333333......
[Writing as a decimal number.]

So, the decimal that represents the fraction of the alphabet A in the pie diagram is 0.333333......

98.
Jim was given 12 problems to solve as homework, of which he solved 4 in the evening and the rest at night. Find the decimal equivalent to the fraction of problems he solved at night to the total number of problems he had for homework. a. 0.66 b. 0.46 c. 0.86 d. None of the above

Solution:

The number of problems Jim solved in the night = the total number of homework problems he had - the number of problems he solved in the evening.

12 - 4
[Substitute the values.]

= 8
[Subtract.]

The fraction of problems he solved in the night to the total number of homework problems he had = the number of problems he solved in the night / the total number of homework problems he had.

812
[Substitute the values.]

= 0.66
[Convert the fraction into a decimal number.]

The decimal that is equivalent to the fraction of problems he solved in the night to the total number of homework problems he had is 0.66.

99.
A school organized a car wash to raise funds for a charity. Josh had to wash 37 cars. He washed 9 out of 37 cars. Write the rounded decimal number which represents the fraction of cars that are yet to be washed. a. 1.0 b. 0.8 c. 1.2 d. None of the above

Solution:

The number of cars that were left for Josh to wash = the total number of cars that he had to wash - the number of cars he finished washing.

= 37 - 9
[Substitute the values.]

= 28
[Subtract.]

The fraction of cars to be washed = (the number of cars to be washed) / (the total number of cars that he had to wash).

= 2837
[Substitute the values.]

» 0.8
[Convert the fraction into a decimal number.]

So, the decimal number that represents the fraction of cars to be washed is 0.8.

100.
A theater owner sells tickets of price $4 with a discount of$1. Which of the following decimal numbers is equivalent to the fraction representing the new price? a. 1.85 b. 0.95 c. 0.75 d. 0.55

Solution:

The new price of the ticket = the old price of the ticket - the discount on the price of the ticket.

= $4 -$1
[Substitute the values.]

= \$3
[Subtract.]

The fraction representing the new price of the ticket = (the new price of the ticket) / (the old price of the ticket).

= 34
[Substitute the values.]

= 0.75
[Convert the fraction into a decimal number.]

So, the decimal number 0.75 is equivalent to the fraction representing the new price of the ticket.