**Recurring decimals to fractions :**

"Converting recurring decimals to fractions" is a much required stuff for the students who study high school math.

Here, we are going to see, how to convert recurring decimals to fractions step by step.

**Step 1 : **

Let x = Given decimal number

For example,

If the given decimal number is 2.0343434.........

then, let x = 2.0343434...........

**Step 2 : **

Identify the repeated pattern

For example,

In 2.0343434..........., the repeated pattern is 34

(Because 34 is being repeated)

**Step 3 :**

Identify the first repeated pattern and second repeated pattern as as explained in the example given below.

**Step 4 :**

Count the number of digits between the decimal point and first repeated pattern as given in the picture below.

**Step 5 :**

Since there is 1 digit between the decimal point and the first repeated pattern, we have to multiply the given decimal by 10 as given in the picture below.

(If there are two digits -----------> multiply by 100,

three digits -----------> multiply by 1000 and so on )

**Note : **

In (1), we have only repeated patterns after the decimal.

**Step 6 : **

Count the number of digits between the decimal point and second repeated pattern as given in the picture below.

**Step 7 :**

Since there are 3 digits between the decimal point and the second repeated pattern, we have to multiply the given decimal by 1000 as given in the picture below.

**Note :**

In (2), we have only repeated patterns after the decimal.

**Step 8 :**

Now, we have to subtract the result of step 5 from step 7 as given in the picture below.

Now we got the fraction which is equal to the given decimal

**Problem 1 :**

Write the following recurring decimal as a fraction :

32.03256256256..........

**Solution : **

Let X = 32.03256256256.............

Here, the repeated pattern is 256

No. of digits between the 1st repeated pattern and decimal = 2

So, multiply the given decimal by 100. Then, we have

100X = 3203.256256256...............----------(1)

No. of digits between the 2nd repeated pattern and decimal = 5

So, multiply the given decimal by 100000. Then, we have

100000X = 3203256.256256256...............----------(2)

(2) - (1) --------> 99900X = 3200053

X = 3200053 / 99900

Hence, 32.03256256256.......... = 3200053 / 99900

**Problem 2 :**

Write the following recurring decimal as a fraction :

2.03323232..........

**Solution : **

Let X = 2.03323232.............

Here, the repeated pattern is 32

No. of digits between the 1st repeated pattern and decimal = 2

(Here, the first repeated pattern starts after two digits of the decimal)

So, multiply the given decimal by 100. Then, we have

100X = 203.323232...............----------(1)

No. of digits between the 2nd repeated pattern and decimal = 4

So, multiply the given decimal by 10000. Then, we have

10000X = 20332.323232...............----------(2)

(2) - (1) --------> 9900X = 20129

X = 9900 / 20129

Hence, 2.03323232.......... = 9900 / 20129

**Problem 3 :**

Write the following recurring decimal as a fraction :

0.252525..........

**Solution : **

Let X = 0.252525.............

Here, the repeated pattern is 25

No. of digits between the 1st repeated pattern and decimal = 0

So, multiply the given decimal by 1. Then, we have

X = 0.252525...............----------(1)

No. of digits between the 2nd repeated pattern and decimal = 2

So, multiply the given decimal by 100. Then, we have

100X = 25.252525...............----------(2)

(2) - (1) --------> 99X = 25

X = 25 / 99

Hence, 0.252525.......... = 25 / 99

**Problem 4 :**

Write the following recurring decimal as a fraction :

3.3333..........

**Solution : **

Let X = 3.3333.............

Here, the repeated pattern is 3

No. of digits between the 1st repeated pattern and decimal = 0

(Here, the first repeated pattern is "3" which comes right after the decimal point)

So, multiply the given decimal by 1. Then, we have

X = 3.3333...............----------(1)

No. of digits between the 2nd repeated pattern and decimal = 1

(Here, the second repeated pattern is "3" which comes one digit after the decimal point)

So, multiply the given decimal by 10. Then, we have

10X = 33.3333...............----------(2)

(2) - (1) --------> 9X = 30

X = 30 / 9 = 10 / 3

Hence, 3.3333.............. = 10 / 9

After having gone through the stuff given above, we hope that the students would have understood "Recurring decimals to fractions".

Apart from the stuff given above, if you want to know more about "Recurring decimals to fractions", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**