Subscribe to our YouTube channel for the latest videos, updates, and tips.


Conversion of Mixed Recurring Decimals into Vulgar Fractions

Follow the steps for the conversion of mixed recurring decimals into vulgar fractions:

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

(ii) Now, find the number of digits having no bar after the decimal point.

(iii) Suppose there are n-digits without bar, multiply both sides by 10n, so that only the repeating decimal digit is on the right side of the decimal point.

(iv) Now write the repeating digits at least twice.

(v) Now, find the number of digits having bar after the decimal point.

(vi) Suppose there are n-digits having bar, multiply both sides by 10n.

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

(viii) Then divide both the sides of the equation by the coefficient of x.

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

Worked-out examples for the conversion of mixed recurring decimals into vulgar fractions:

1. Express 0.18 as vulgar fraction.

Solution:

x = 0.18

Multiply both sides by 10 (Since number of digits without bar is 1)

10x = 1.8

10x = 1.88…… ---------- (i)

10 × 10x = 1.88…… × 10 (Since number of digits having bars is 1)

100x = 18.8….. ------------- (ii)

Subtracting (i) from (ii)

100x - 10x = 18.8 - 1.8

90x = 17

x = 17/90

Therefore, the vulgar fraction = 17/90


2. Express 0.23 as vulgar fraction.

Solution:

x = 0.23

Multiply both sides by 10 (Since number of digits without bar is 1)

10x = 2.3

10x = 2.33…… ---------- (i)

10 × 10x = 2.33…… × 10 (Since number of digits having bars is 1)

100x = 23.3….. ------------- (ii)

Subtracting (i) from (ii)

100x - 10x = 23.3 - 2.3

90x = 21

x = 21/90

x = 7/30

Therefore, the vulgar fraction = 7/30



3. Express 0.43213 as vulgar fraction.

Solution:

x = 0.43213

Multiply both sides by 100 (Since number of digits without bar is 2)

100x = 43.213

100x = 43.213213…… ---------- (i)

100 × 1000x = 43.213…… × 1000 (Since number of digits having bars is 3)

100000x = 43213.213….. ------------- (ii)

Subtracting (i) from (ii)

100000x - 100x = 43213.213 - 43.213213

99900x = 43170

x = 43170/99900

x = 4317/9990

Therefore, the vulgar fraction = 4317/9990


Shortcut method for solving the problems on conversion of mixed recurring decimals into vulgar fractions:

The difference between the number formed by all the digits in decimal part and the number formed by digits that are not repeated, gives the numerator of the vulgar fraction and for its denominator the number formed by as many nines as there are recurring digits which are repeated followed by as many zeros as the number of non-repeating or non-recurring digits.

For example;

Express 0.123 as vulgar fraction.
Numerator = 123 - 12 = 111

Denominator = one nine (as there are one recurring digit) followed by two zeros (as there are two non-recurring digits) = 900

Required fraction = 111/900 (reduce to its simplest form)

Therefore, the vulgar fraction = 37/300

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

From Conversion of Mixed Recurring Decimals into Vulgar Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Calculating Profit Percent and Loss Percent | Profit and Loss Formulas

    Jun 12, 25 12:48 PM

    In calculating profit percent and loss percent we will learn about the basic concepts of profit and loss. We will recall facts and formula while calculating profit percent and loss percent. Now we wil

    Read More

  2. Word Problems on Profit and Loss Worksheet |Cost Price |Selling Price

    Jun 11, 25 04:26 PM

    Word Problems on Profit and Loss Worksheet
    In word problems on profit and loss worksheet you will get different types of problems on cost price and selling price, profit and loss, calculating profit o loss, calculating selling price and cost p…

    Read More

  3. Round off to Nearest 1000 |Rounding Numbers to Nearest Thousand| Rules

    Jun 11, 25 03:12 PM

    Round off to Nearest 1000
    Round off to nearest 1000 is discussed here. While rounding off to the nearest 1000, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the d…

    Read More

  4. Round off to Nearest 100 | Rounding Numbers To Nearest Hundred | Rules

    Jun 11, 25 03:13 AM

    Round off to Nearest 100
    While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the…

    Read More

  5. Round off to Nearest 10 |How To Round off to Nearest 10?|Rounding Rule

    Jun 10, 25 05:36 PM

    Rounding to the Nearest 10
    Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number…

    Read More