﻿ Terminating and Repeating Decimals Worksheet | Problems & Solutions # Terminating and Repeating Decimals Worksheet

Terminating and Repeating Decimals Worksheet
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1.
Which of the following is a terminating decimal? a. $\frac{1}{12}$ b. $\frac{3}{2}$ c. $\frac{3}{9}$ d. $\frac{2}{3}$

#### Solution:

For 2 / 3, the quotient is 0.66666. . . and the digit 6 is repeating.

For 3 / 9, the quotient is 0.33333. . . and the digit 3 is repeating.

For 1 / 12, the quotient is 0.08333. . . and the digit 3 is repeating.

For 3 / 2, the quotient is 1.5.

A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.

So, 3 / 2 is a terminating decimal.

2.
Which of the following is a repeating decimal? a. $\frac{1}{4}$ b. $\frac{1}{11}$ c. $\frac{5}{10}$ d. $\frac{8}{5}$

#### Solution:

When a digit or sequence of digits keep repeating, it is a repeating decimal.

For 8 / 5, when 8 is divided by 5 the quotient is 1.6.

For 1 / 4, when 1 is divided by 4 the quotient is 0.25.

For 5 / 10, when 5 is divided by 10 the quotient is 0.2.

For 1 / 11, when 1 is divided by 11, the quotient is 0.090909. . . and the digits 09 are repeating.

Therefore, 1 / 11 is a repeating decimal.

3.
Identify a repeating decimal. a. $\frac{3}{8}$ b. $\frac{1}{15}$ c. $\frac{3}{10}$ d. $\frac{4}{5}$

#### Solution:

When a digit or sequence of digits keep repeating, it is a repeating decimal.

For 4 / 5, when 4 is divided by 5 the quotient is 0.8.

For 3 / 8, when 3 is divided by 8 the quotient is 0.375.

For 3 / 10, when 3 is divided by 10 the quotient is 0.3.

For 1 / 15, when 1 is divided by 15, the quotient is 0.06666. . . and the digit 6 is repeating.

Therefore, 1 / 15 is a repeating decimal.

4.
Identify a terminating decimal. a. $\frac{5}{9}$ b. $\frac{1}{9}$ c. $\frac{6}{8}$ d. $\frac{5}{3}$

#### Solution:

For 1 / 9, the quotient is 0.11111. . . and the digit 1 is repeating.

For 5 / 9, the quotient is 0.55555. . . and the digit 5 is repeating.

For 5 / 3, the quotient is 1.66666. . . and the digit 6 is repeating.

For 6 / 8, the quotient is 0.75.

A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.

So, 6 / 8 is a terminating decimal.

5.
Which of the following gives you a terminating decimal? a. 11 ÷ 12 b. 12 ÷ 15 c. 4 ÷ 3 d. 10 ÷ 9

#### Solution:

For 4 ÷ 3, the quotient is 1.33333. . . and the digit 3 is repeating.

For 11 ÷ 12, the quotient is 0.91666. . . and the digit 6 is repeating.

For 10 ÷ 9, the quotient is 1.11111. . . and the digit 1 is repeating.

For 12 ÷ 15, the quotient is 0.8.

A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.

So, 12 ÷ 15 is a terminating decimal.

6.
Pick the non-repeating decimal. a. 0.0777... b. 0.033... c. 0.03 d. 0.0303...

#### Solution:

When a digit or sequence of digits keep repeating, it is a repeating decimal.

In the choices, all are repeating decimals except 0.03.

0.03 is the non repeating decimal.

7.
Identify the terminating decimal. a. 0.0545454... b. 0.0655... c. 0.055 d. 0.155...

#### Solution:

A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.

Among the choices, except 0.055, all are repeating decimals.

So, 0.055 is a terminating decimal.

8.
Find the quotient of 12.4 ÷ 3 and write what type of quotient it is. a. 4.1333, repeating decimal b. 4.1333, terminating decimal c. 4.1, repeating decimal d. None of the above

#### Solution:

12.4 ÷ 3
[Given expression.]

Divisor = 3 and dividend = 12.4. Quotient = 4.1333... and the digit 3 keeps repeating. It is a repeating decimal.

9.
Find the missing divisor in the table.  a. 0.0001 b. 100 c. 10 d. 0.001

#### Solution:

The sequence of divisors is 100, 10, 1, 0.1, 0.01 and the next number is 0.001.

The missing divisor = 0.001.

Check by dividing 44 by 0.001, we get 44 / 0.001 = 44000.

10.
In which of the cases is the quotient a repeating decimal?
i. 5 ÷ 100
ii. 5 ÷ 10
iii. 5 ÷ 0.001 a. Case (iii) is repeating b. None of the cases is repeating c. Case (i) is repeating d. Case (ii) is repeating

#### Solution:

5 ÷ 100
[Consider case (i).]

Divisor = 100 and dividend = 5. [Place the decimal point in quotient. Then divide.]

The quotient is 0.05 and for case (ii) quotient is 0.5 and for case (iii) quotient is 5000.

No quotient is repeating.