# CONVERTING RECURRING DECIMALS TO FRACTIONS WORKSHEET

Converting Recurring Decimals to Fractions Worksheet :

Worksheet given in this section will be much useful for the students who would like to practice problems on converting recurring decimals into fractions.

Before look at the worksheet, if you would like to learn, how to convert recurring decimals into fractions,

## Converting Recurring Decimals to Fractions Worksheet - Problems

Problem 1 :

Covert the given repeating decimal into fraction

32.03256256256..........

Problem 2 :

Covert the given repeating decimal into fraction

0.01232222........

Problem 3 :

Covert the given repeating decimal into fraction

2.03323232..........

Problem 4 :

Covert the given repeating decimal into fraction

0.252525..........

Problem 5 :

Covert the given repeating decimal into fraction

3.3333..........

Problem 6 :

Covert the given repeating decimal into fraction

1.023562562562..........

## Converting Recurring Decimals to Fractions Worksheet - Solutions

Problem 1 :

Covert the given repeating decimal into 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)

Subtracting (1) from (2), we get

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

x  =  3200053/99900

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

Problem 2 :

Covert the given repeating decimal into fraction

0.01232222........

Solution :

Let x  =  0.01232222.............

Here, the repeated pattern is 2

No. of digits between the 1st repeated pattern and decimal  =  4

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

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

10000X  =  123.2222...............-----(1)

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

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

100000x  =  1232.2222...............-----(2)

Subtracting (1) from (2), we get

(2) - (1) -----> 90000x  =  1109

x  =  1109/90000

Hence, 0.01232222........... =  1109/90000.

Problem 3 :

Covert the given repeating decimal into 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)

Subtracting (1) from (2), we get

(2) - (1) -----> 9900x  =  20129

x  =  9900/20129

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

Problem 4 :

Covert the given repeating decimal into 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)

Subtracting (1) from (2), we get

(2) - (1) --------> 99x  =  25

x  =  25/99

Hence, 0.252525.......... =  25/99.

Problem 5 :

Covert the given repeating decimal into 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)

Subtracting (1) from (2), we get

(2) - (1) -----> 9x  =  30

x  =  30/9  =  10/3

Hence, 3.3333.............. =  10/3.

Problem 6 :

Covert the given repeating decimal into fraction

1.023562562562..........

Solution :

Let x  =  1.023562562562.............

Here, the repeated pattern is 562

No. of digits between the 1st repeated pattern and decimal  =  3

So, multiply the given decimal by 1000. Then, we have

1000x  =  1023.562562562...............-----(1)

No. of digits between the 2nd repeated pattern and decimal  =  6

So, multiply the given decimal by 1000000. Then, we have

1000000x  =  1023562.562562562...............-----(2)

Subtracting (1) from (2), we get

(2) - (1) -----> 999000x  =  1022538

x  =  1022539/999000

Hence, 1.023562562562.......... =  1022539/999000

After having gone through the stuff and examples, we hope that the students would have understood, how to convert recurring decimals to fractions.

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