Terminating and Repeating Decimals Worksheet

Terminating and Repeating Decimals Worksheet
  • Page 1
 1.  
Which of the following is a terminating decimal?
a.
1 12
b.
3 2
c.
3 9
d.
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.


Correct answer : (2)
 2.  
Which of the following is a repeating decimal?
a.
1 4
b.
1 11
c.
5 10
d.
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.


Correct answer : (2)
 3.  
Identify a repeating decimal.
a.
3 8
b.
1 15
c.
3 10
d.
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.


Correct answer : (2)
 4.  
Identify a terminating decimal.
a.
5 9
b.
1 9
c.
6 8
d.
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.


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 44 / 0.001 = 44000.


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
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)

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