**Converting Recurring Decimals to Fractions Worksheet :**

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

**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

1.023562562562..........

**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

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, "Converting recurring decimals to fractions worksheet"

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