#### Solved Examples and Worksheet for Fractions as Terminating or Repeating Decimals

Q1Identify the terminating decimal.
A. 0.0545454...
B. 0.055
C. 0.0655...
D. 0.155...

Step: 1
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
Step: 2
Among the choices, except 0.055, all are repeating decimals.
Step: 3
So, 0.055 is a terminating decimal.
Q2Convert 1311 as a decimal and find the digits that repeat in the quotient.
A. 11
B. 2
C. 8
D. 18

Step: 1
1311 = 1.181818...
[Divide.]
Step: 2
= 1.18¯
[Place the bar on 18 since it repeats.]
Step: 3
The block of digits that repeat is 18.
Q3Which of the following fractions is a terminating decimal?
(I) 49
(II) 65
(III) 611

A. Only (I)
B. Only (II)
C. Both (I) and (III)
D. Both (II) and (III)

Step: 1
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.
Step: 2
Consider the first fraction, 49 :
49 = 0.44444444...
[Convert the fraction into a decimal number.]
Step: 3
Consider the second fraction, 65 :
65 = 1.20
[Convert the fraction into a decimal number.]
Step: 4
Consider the third fraction, 611:
611= 0.54545454...
[Convert the fraction into a decimal number.]
Step: 5
Among the fractions, the second fraction is a terminating decimal.
Correct Answer is :   Only (II)
Q4Which of the following is a repeating decimal?
i. 33 ÷ 6
ii.6 ÷ 33

A. (ii)
B. (i)
C. Both (i) and (ii)
D. None of the above

Step: 1
33 ÷ 6
[Divide 33 with 6.] Step: 2
The quotient obtained after dividing 33 with 6 is 5.5, which is a terminating decimal.
Step: 3
6 ÷ 33
[Divide 6 with 33.]
Step: 4
After dividing 6 with 33, the quotient obtained is 0.181818...
Step: 5
Since 18 is coming repetatively in quotient, 6 ÷ 33 is a repeating decimal.
Step: 6
So, (ii) is a repeating decimal.
Q5Identify a rational number that is a repeating decimal.

A. 522
B. 364
C. 34
D. 68

Step: 1
522 = 0.22727272. . . is a rational number with a repeating decimal.
Q6Identify a terminating decimal.

A. 49
B. 510
C. 19
D. 43

Step: 1
For 19, the quotient is 0.11111. . . and the digit 1 is repeating.
Step: 2
For 49, the quotient is 0.444. . . and the digit 4 is repeating.
Step: 3
For 43, the quotient is 1.333. . . and the digit 3 is repeating.
Step: 4
For 510, the quotient is 0.5.
Step: 5
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
Step: 6
So, 510 is a terminating decimal.
Q7Which of the following is a terminating decimal?
A. 17
B. 29
C. 13
D. 14

Step: 1
For 17, the quotient is 0.14285714285714. . . . . the digits 142857 are repeating
Step: 2
For 13 the quotient is 0.3333. . . . . the digit is 3 is repeating
Step: 3
For 29 , the quotient is 0.2222 . . . . . . the digit 2 is repeating
Step: 4
For 14, the quotient is 0.25
Step: 5
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
Step: 6
So, 14is a terminating decimal
Q8Identify a terminating decimal.

A. 1.3333 . . . . .
B. 0.2
C. 0.25555 . . . . .
D. 0. 888 . . . . .

Step: 1
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
Step: 2
Therefore, 0.2 is a terminating decimal.
Q9Identify a terminating decimal.
A. 5 ÷ 2
B. 10 ÷ 3
C. 2 ÷ 3
D. 4 ÷ 9

Step: 1
For 2 ÷ 3, the quotient is 0.66666. . . and the digit 6 is repeating.
Step: 2
For 4 ÷ 9, the quotient is 0.44444. . . and the digit 4 is repeating.
Step: 3
For 10 ÷ 3, the quotient is 3.33333. . . and the digit 3 is repeating.
Step: 4
For 5 ÷ 2, the quotient is 2.5.
Step: 5
A decimal that terminates or stops after a finite number of decimal places is a terminating decimal.
Step: 6
So, 5 ÷ 2 is the terminating decimal.
Correct Answer is :   5 ÷ 2