**Introduction**

**Repeating decimals to fractions:-**

**repeating decimals**.

## Repeating Decimals to Fractions – Conversion

The repeating decimals can be converted into fractions.

# Convert 0.7777……. into fraction

Solution:-

Let x = 0.7777

step1 multiply x by 10

Then 10x = 7.777

step 2 subtract x from 10 x

Then 10x – x = 7.777 – 0.777

9x = 7.000

Step 3 Dividing both sides by 9 we get x = 7/9

Answer 0.7777…… = 7/9

#Convert 0.2424… to fractions.

Let x = 0.2424

Step1 multiply x by 100

Then 100x = 24.2424

Step2 subtract x from 100x

100x – x = 24.2424 – 0.2424

99x = 24

Step3 Divide both sides by 99

x = 24/99 which on **simplification** gives 8/33

Hence 0.2424…. = 8/33

#Convert 0.27777,,,,, into fractions

Let x = 0.27777

step1 multiply x by 10

then 10x = 2.7777

step 2 multiply x by 100

and 100x = 27.777

step 3 subtract 10x from 100x

100x – 10 x = 27.777 – 2.777

90x = 25

Step 4 divide both sides by 90

x = `25/90 = 5/18`

Answer 0.27777 = `5/18`

# Convert 0.35656…. into fractions

Let x = 0.35656

Then 10x = 3.5656

1000x = 356.5656

1000x – 10x = 356.5656 – 3.5656

990x = 353

x = `353/990`

# Convert 0.3333 t fractions

Let x = 0.333

10x = 3.33

10x – x= 3.33 – 0.33

9x = 3

x = `3/9 = 1/3`

Hence o,3333 = `1/3`

# Convert 0.416666… to fractions

Let x = 0.41666

Then 100x = 41.666 and 1000x = 416.666

1000x – 100x = 416.666 – 41.666

900x = 375

x =`375/900 = 5/12`

Answer 0.416666….. = `5/12`

#Convert 0.888888…. into fractions.

Let x = 0.88

Then 10 x = 8.88

10x – x = 8.88 – 0.88

9x = 8

x = 8/9

# Convert 0.4646…. as fraction

Let x = 0.4646

100x = 46.4646

100x – x = 46.4646 – 0.4646

99x = 46

x = `46/99`

Answer 0.4646 =`46/99`

# Convert 0.717171 into fraction

Let x = 0.717171

100x= 71.7171

100x – x = 71.7171 – 0.7171

99x = 71

x =`71/99`

## Repeating Decimal to Fraction-practice Problems

#Convert 0.5555…. into fraction (Ans:`5/9` )

#Convert 0.232323…into fraction (Ans:`23/99` )

#Convert 0.757575..into fraction (Ans:`25/33` )

#Convert 0.522522..into fraction (Answer:`58/111` )

#Convert 0.057057..into fraction (Answer:`19/333` )