Conversion of Mixed Recurring Decimals into Vulgar Fractions

Conversion of Mixed Recurring Decimals into Vulgar Fractions – Definition, Examples | How to Convert a Mixed Recurring Decimal to a Vulgar Fraction?

Struggling with the conversion of a Mixed Repeating Decimal to Vulgar Fraction? If so, don’t panic as we are with you in this and we will provide you complete information on Procedure for Converting Mixed Recurring Decimal to Vulgar Fraction, Shortcut Method, etc. Solved Examples provided for changing from Mixed Repeating Decimal to Vulgar Fraction will help you to understand the concept well and solve your related problems easily.

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How to Convert a Mixed Recurring Decimal into a Vulgar Fraction?

Follow the simple and easy guidelines listed below for converting a mixed recurring decimal to a vulgar fraction. They are in the following fashion

  • First, write down the decimal form by removing the bar on the repeating digits and say it is x
  • Now, find out the number of digits that have no bar on them after the decimal point.
  • If there are n-digits without bar multiply both sides with 10n in a way that only the repeating digit is on the right side of the decimal point…..(1)
  • Now, write down the repeating digits at least twice.
  • If you have n-repeating digits i.e. with a bar multiply both sides with¬†10n…..(2)
  • Subtract the number obtained in Step 1 from Step 2.
  • Divide both sides of the equation with the coefficient of x.
  • The resultant fraction form in the lowest terms is known as the vulgar fraction.

Worked Out Examples on Changing a Mixed Recurring Decimal to a Vulgar Fraction

1. Express 0.3\(\overline{4}\) as a Vulgar Fraction?

Solution:

x=0.3\(\overline{4}\)

Multiply with 10 on both sides since the number of digits after the decimal point not having a bar on them is 1.

10x=3.\(\overline{4}\)

10x=3.44444………(1)

Check for the number of digits having a bar. Since we have 1 repeating digit having bar we multiply with 10

10*10x=3.4444…..*10

100x=34.4444…….(2)

Subtract (1) from (2) we have

100x-10x=34.4444…-3.4444…

90x=31

x=\(\frac { 31 }{ 90 } \)

Therefore, 0.3\(\overline{4}\) expressed as vulgar fraction is \(\frac { 31 }{ 90 } \)

2. Express 0.53\(\overline{212}\) as a Vulgar Fraction?

Solution:

x=0.53\(\overline{212}\)

Multiply with 102 on both sides since the number of digits after the decimal point not having a bar on them is 2.

100x=53.212212…….(1)

Multiply with 103 on both sides since the number of digits after the decimal point having a bar on them is 3.

100x*1000=53.212212……*1000

100000x=53212.212212…….(2)

Subtract (1) from (2) we have

100000x-100x=53212.212212…….-53.212212……

99900x=53159

x=\(\frac { 53159}{ 99900 } \)

Therefore, 0.53\(\overline{212}\) expressed as vulgar fraction is \(\frac { 53159}{ 99900 } \)

Shortcut Method for Converting Mixed Recurring Decimal into a Vulgar Fraction

You can go with the shortcut and easy method to change between a mixed recurring decimal to a vulgar fraction easily. They are in the following fashion

  • The numerator in the vulgar fraction is obtained by doing the difference between all the digits after the decimal point and the digits that aren’t repeated.
  • However, the denominator will have the value equal to as many nines are in the repeating digits followed by as many number of zeros as in the non-repeating digits.

Solved Examples for Converting Mixed Repeating Decimals to Vulgar Fraction

1. Express 0.23\(\overline{5}\) as a Vulgar Fraction?

Solution:

The numerator in the vulgar fraction is obtained by finding the difference between all digits of the decimal part and the non-repeated digits.

Numerator =235-23

= 212

The denominator of the vulgar fraction is obtained by placing as many nines as in the repeating digits followed by the number of zeros in the non-repeating digits.

Denominator = 900

Thus, 0.23\(\overline{5}\) expressed as vulgar fraction is \(\frac { 212 }{ 900 } \)

FAQs on Conversion of Mixed Recurring Decimal to Vulgar Fraction

1. What is a Mixed Recurring Decimal?

A Decimal Number in which at least one of the digits is non-repeated and some other digits repeat is known as a Mixed Recurring Decimal.

2. What is a Vulgar Fraction?

A fraction in which both the numerator and denominator are fractions is known as a Vulgar Fraction. The other name for Vulgar Fraction is Common Fraction.

3. How do you Convert a Mixed Repeating Decimal to a Vulgar Fraction?

The numerator in a vulgar fraction is nothing but the difference between all the digits after the decimal point to the digits that are not repeated. However, you can obtain the denominator by simply placing as many nines are there in the repeating digits followed by as many zeros as in the digits that are non-repeated.

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