Conversion of Pure Recurring Decimal into Vulgar Fraction

Follow the steps for the conversion of pure recurring decimal into vulgar fraction:

(i) First write the decimal form by removing the bar from the top and put it equal to n (any variable).

(ii) Then write the repeating digits at least twice.

(iii) Now find the number of digits having bars on their heads.

If the repeating decimal has 1 place repetition, then multiply both sides by 10.

If the repeating decimal has 2 place repetitions, then multiply both sides by 100.

If the repeating decimal has 3 place repetitions, then multiply both sides by 1000 and so on.

(iv) Then subtract the number obtained in step (i) from the number obtained in step (ii).

(v) Then divide both the sides of the equation by the coefficient of n.

(vi) Therefore, we get the required vulgar fraction in the lowest form.


Worked-out examples for the conversion of pure recurring decimal into vulgar fraction:

1. Express 0.4 as a vulgar fraction.

Solution:

Let n = 0.4

n = 0.444 ----------- (i)

Since, one digit is repeated after the decimal point, so we multiply both sides by 10.

Therefore, 10n = 4.44 ----------- (ii)

Subtracting (i) from (ii) we get;

10n - n = 4.44 - 0.44

9n = 4

n = 4/9 [dividing both the sides of the equation by 9]

Therefore, the vulgar fraction = 4/9


2. Express 0.38 as a vulgar fraction.

Solution:

Let n = 0.38

n = 0.3838 ----------------- (i)

Since, two digits are repeated after the decimal point, so we multiply both sides by 100.

Therefore, 100n = 38.38 ----------------- (ii)

Subtracting (i) from (ii) we get;

100n - n = 38.38 - 0.38

99n = 38

n = 38/99

Therefore, the vulgar fraction = 38/99


3. Express 0.532 as a vulgar fraction.

Solution:

Let n = 0.532

n = 0.532532 ----------------- (i)

Since, three digits are repeated after the decimal point, so we multiply both sides by 1000.

Therefore, 1000n = 532.532 ----------------- (ii)

Subtracting (i) from (ii) we get;

1000n - n = 532.532 - 0.532

999n = 532

n = 532/999

Therefore, the vulgar fraction = 532/999


Shortcut method for solving the problems on conversion of pure recurring decimal into vulgar fraction:

Write the recurring digits only once in the numerator and write as many nines in the denominator as is the number of digits repeated.

For example;

(a) 0.5

Here numerator is the period (5) and the denominator is 9 because there is one digit in the period.

= 5/9

(b) 0.45

Numerator = period = 45

Denominator = as many nines as the number of digits in the denominator

= 45/99

Related Concept

Decimals

Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

Rounding Decimals to the Nearest Whole Number

Rounding Decimals to the Nearest Tenths

Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

Simplify Decimals Involving Addition and Subtraction Decimals

Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number


7th Grade Math Problems

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