Recurring Decimals to Fractions : Solution

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Examples : What is a Recurring Decimal ? : Click Here

Q. Write the recurring decimal 0.2(6) as fraction.

Solⁿ: Repeating part = 6
(1 repeating digit → denominator = 9 & 1 non-repeating digit → denominator = 0)

So, 0.2(6) = 26-2/90 = 24/90 or12/45 or 4/15

Ans: 24/90 or12/45 or 4/15

Q. Write the recurring decimal 0.1(7) as fraction.

Solⁿ: Repeating part = 7
(1 repeating digit → denominator = 9 & 1 non-repeating digit → denominator = 0)

So, 0.1(7) = 17-1/90 = 16/90 = 8/45

Ans: 8/45

Q. Write the recurring decimal 0.6(7) as fraction.

Solⁿ: Repeating part = 7
(1 repeating digit → denominator = 9 & 1 non-repeating digit → denominator = 0)

So, 0.6(7) = 67-6/90 = 61/90

Ans: 61/90

Q. Write the recurring decimal 0.(04) as fraction.

Solⁿ: Repeating part = 04
(2 repeating digit → denominator = 99)

So, 0.(04) = 4/99

Ans: 4/99

What is a Recurring Decimal ? : Click Here

Q. Write the recurring decimal 0.(37) as fraction.

Solⁿ: Repeating part = 37
(2 repeating digit → denominator = 99)

So, 0.(37) = 37/99

Ans: 37/99

Q. Write the recurring decimal 0.(7) as a fraction.

Solⁿ: For 1 repeating digit → put 9 in the denominator.

Repeating part = 7

So, 0.(7) = 7/9

Ans: 0.(7) = 7/9

Q. Write the recurring decimal 0.(27) as a fraction.

Solⁿ: Repeating part = 27
(2 repeating digit → denominator = 99)

So, 0.(27) = 27/99

Simplify: 27/99 = 3/11

Ans: 3/11

Q. Convert 2/9 to a decimal

Solⁿ: 2 ÷ 9 = 0.222… This means the digit 2 repeats forever.

This is a recurring decimal (digit 2 is repeating).

Ans: recurring 0.(2) repeating

Q. Convert 4/11 to a decimal

Solⁿ: 4 ÷ 11 = 0.363636… This means the digit .36 repeats forever.

This is a recurring decimal (digit .36 is repeating).

Ans: recurring 0.(36) thirty-six repeating

What is a Recurring Decimal ? : Click Here

Q. Convert 5/6 to a decimal

Sol^n: 5 ÷ 6 = 0.8333…

Ans: recurring 0.8(3) repeating

Q. Prove: recurring decimal 0.(8) repeating = 8/9  

Solⁿ

For 1 repeating digit → put 9 in the denominator.

Repeating part = 8

So, 0.(8) = 8/9

Ans: 0.(8) = 8/9

What is a Recurring Decimal ? : Click Here

Q. Write 0.16 as a fraction in its simplest form.

Sol^{n :}

Write as fraction: 0.16 = 16​/100

Simplify dividing by 4 : 16/100 ​= 4​/25

Ans: 0.16 = 4/25

What is a Recurring Decimal ? : Click Here

Q. Convert the recurring decimal 0.1(6) into a fraction.

Solⁿ :

Repeating part = 6
(1 repeating digit → denominator = 9 & 1 non-repeating digit → denominator = 0)

So, 0.1(6) = 16-1/90 =15/90

Simplify: 15/90= = 1/6

Ans: 1/6

Q. Convert the recurring decimal 0.4(2) into a fraction.

Solⁿ :

Repeating part = 2
(1 repeating digit → denominator = 9 & 1 non-repeating digit → denominator = 0)

So, 0.4(2) = 42-4/90 =38/90

Simplify: 38/90= = 19/45

Ans: 0.4(2) = 19/45

Q. Prove algebraically that the recurring decimal 0.2(3) can be written as 7/ 30 

Solⁿ 

Repeating part = 3
(1 repeating digit → denominator = 9 & 1 non-repeating digit → denominator = 0)

So, 0.2(3) = 23-2/90 =21/90

Simplify: 21/90 = 7/30

Ans: 0.2 repeating 3 = 7/30

What is a Recurring Decimal ? : Click Here

Q. Prove algebraically that the recurring decimal 0.4(7) can be written as 43/90.

Solⁿ

Repeating part = 7
(1 repeating digit → denominator = 9 & 1 non-repeating digit → denominator = 0)

So, 0.4(7) = 47-4/90 = 43/90

Ans: 0.4(7) = 43/90

Short Trick - 0.4(7) = 47- 4/90 = 43/90

Q. Write the recurring decimal 0.4(19) as fraction.

Solⁿ: Repeating part = 19
(2 repeating digit → denominator = 99 & 1 non-repeating digit → denominator = 0)

So, 0.4(19) = 419-4/990 = 415/990 or 83/198

Ans: 415/990 or 83/198

Q. Write the recurring decimal 0.6(21) as fraction.

Solⁿ: Repeating part = 21(2 repeating digit → denominator = 99)

So, 0.6(21) = 621-6/990 = 615/990 or 41/66

Ans: 615/990 or 41/66