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Terminating and Repeating Decimals Worksheet
Practice Problems
2 3
For3 9
For1 12
For3 2
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
So,3 2
For8 5
For1 4
For5 10
For1 11
Therefore,1 11
For4 5
For3 8
For3 10
For1 15
Therefore,1 15
1 9
For5 9
For5 3
For6 8
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
So,6 8
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.
In the choices, all are repeating decimals except 0.03.
0.03 is the non repeating decimal.
Among the choices, except 0.055, all are repeating decimals.
So, 0.055 is a terminating decimal.
[Given expression.]
Divisor = 3 and dividend = 12.4.
Quotient = 4.1333... and the digit 3 keeps repeating. It is a repeating decimal.
The missing divisor = 0.001.
Check by dividing 44 by 0.001, we get44 0.001
[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.
Terminating and Repeating Decimals Worksheet
- Page 1
1.
Which of the following is a terminating decimal?
| a. | |||
 | b. | ||
| c. | |||
| d. |
Solution:
ForFor
For
For
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
So,
Correct answer : (2)
2.
Which of the following is a repeating decimal?
| a. | |||
| b. | ||
| c. | |||
| d. |
Solution:
When a digit or sequence of digits keep repeating, it is a repeating decimal.For
For
For
For
Therefore,
Correct answer : (2)
3.
Identify a repeating decimal.
| a. | |||
| b. | ||
| c. | |||
| d. |
Solution:
When a digit or sequence of digits keep repeating, it is a repeating decimal.For
For
For
For
Therefore,
Correct answer : (2)
4.
Identify a terminating decimal.
| a. | |||
| b. | |||
| c. | ||
| d. |
Solution:
ForFor
For
For
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
So,
Correct answer : (3)
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.
Correct answer : (2)
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.
Correct answer : (3)
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.
Correct answer : (3)
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.
Correct answer : (1)
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
Correct answer : (4)
10.
In which of the cases is the quotient a repeating decimal?
i. 5 ÷ 100
ii. 5 ÷ 10
iii. 5 ÷ 0.001
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.
Correct answer : (2)