CONVERTING RECURRING DECIMALS TO FRACTIONS WORKSHEET

Covert the following recurring decimals to fractions :

1)  2.7343434..............

2)  32.03256256256..........

3)  0.01232222........

4)  2.03323232..........

5)  0.252525..........

6)  3.3333..........

7)  1.023562562562..........

8)  0.6666..........

1. Answer :

Let x = 2.7343434..............

The repeated pattern is 34.

There is one digit between the decimal point and 1st repeated pattern, that is 7.

Multiply the given decimal number by 10.

10x = 27.343434..............-----(1)

There are three digits between the decimal point and the 2nd repeated pattern, that is 734.

Multiply the given decimal number by 1000.

1000x = 2734.3434..............-----(2)

Subtract (1) from (2).

90x = 2707

x = 2707/90

2.7343434.............. = 2707/90

2. Answer :

Let x = 32.03256256256.............

The repeated pattern is 256.

There are two digits between the decimal point and 1st repeated pattern, that is 03.

Multiply the given decimal number by 100.

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

There are five digits between the decimal point and the 2nd repeated pattern, that is 03256.

Multiply the given decimal number by 100000.

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

Subtract (1) from (2).

99900x = 3200053

x = 3200053/99900

32.03256256256.......... = 3200053/99900

3. Answer :

Let x = 0.01232222.............

The repeated pattern is 2.

There are four digits between the decimal point and 1st repeated pattern, that is 0123.

Multiply the given decimal number by 10000.

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

There are five digits between the decimal point and the 2nd repeated pattern, that is 01232.

Multiply the given decimal number by 100000.

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

Subtract (1) from (2).

90000x = 1109

x = 1109/90000

0.01232222........... = 1109/90000

4. Answer :

Let x = 2.03323232.............

The repeated pattern is 32.

There are two digits between the decimal point and 1st repeated pattern, that is 03.

Multiply the given decimal number by 100.

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

There are four digits between the decimal point and the 2nd repeated pattern, that is 0332.

Multiply the given decimal number by 10000.

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

Subtract (1) from (2).

9900x = 20129

x = 9900/20129

2.03323232.......... = 9900/20129

5. Answer :

Let x = 0.252525.............

The repeated pattern is 25.

There is no digit between the decimal point and 1st  repeated pattern.

x = 0.252525...............-----(1)

There are two digits between the decimal point and the 2nd repeated pattern, that is 25.

Multiply the given decimal number by 100.

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

Subtract (1) from (2).

99x = 25

x = 25/99

0.252525.......... = 25/99

6. Answer :

Let x = 3.3333.............

The repeated pattern is 3.

There is no digit between the decimal point and 1st  repeated pattern.

x = 3.3333...............-----(1)

There is one digit between the decimal point and the 2nd repeated pattern, that is 3.

Multiply the given decimal number by 10.

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

Subtract (1) from (2).

9x = 30

x = 30/9

x = 10/3

3.3333.............. = 10/3

7. Answer :

Let x = 1.023562562562.............

The repeated pattern is 562.

There are three digits between the decimal point and 1st repeated pattern, that is 023.

Multiply the given decimal number by 1000.

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

There are six digits between the decimal point and the 2nd repeated pattern, that is 023562.

Multiply the given decimal number by 1000000.

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

Subtract (1) from (2).

999000x = 1022538

x = 1022539/999000

1.023562562562.......... = 1022539/999000

8. Answer :

Let x = 0.6666.............

The repeated pattern is 6.

There is no digit between the decimal point and 1st  repeated pattern.

x = 0.6666...............-----(1)

There is one digit between the decimal point and the 2nd repeated pattern, that is 6.

Multiply the given decimal number by 10.

10x = 6.6666...............-----(2)

Subtract (1) from (2).

9x = 6

x = 6/9

x = 2/3

0.6666.......... = 2/3

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