Maths-

General

Easy

Question

# Convert the following fractions to repeating decimals

c)

Hint:

### Divide and find the repeating decimal.

## The correct answer is: 0.3030303030

### Complete step by step solution:

(c) On dividing 10 by 33, we have 0.3030303030.. as the corresponding decimal number.

### Related Questions to study

Maths-

### Convert the following fractions to repeating decimals

b)

Complete step by step solution:

(b) On dividing 7 by 18, we have 0.3888888888.. as the corresponding decimal number.

(b) On dividing 7 by 18, we have 0.3888888888.. as the corresponding decimal number.

### Convert the following fractions to repeating decimals

b)

Maths-General

Complete step by step solution:

(b) On dividing 7 by 18, we have 0.3888888888.. as the corresponding decimal number.

(b) On dividing 7 by 18, we have 0.3888888888.. as the corresponding decimal number.

Maths-

### Convert the following fractions to repeating decimals

a)

Complete step by step solution:

(a) On dividing 11 by 12, we have 0.9166666666.. as the corresponding decimal number.

(a) On dividing 11 by 12, we have 0.9166666666.. as the corresponding decimal number.

### Convert the following fractions to repeating decimals

a)

Maths-General

Complete step by step solution:

(a) On dividing 11 by 12, we have 0.9166666666.. as the corresponding decimal number.

(a) On dividing 11 by 12, we have 0.9166666666.. as the corresponding decimal number.

Maths-

### Convert the following repeating decimals to fractions

d) 3.25252525252...............

Complete step by step solution:

(d) Let x = 0.25252525

Now multiply by 100 on both the sides,

We get, 100x = 25.252525

On subtracting x from both the sides, we have

Now we have a fraction for 0.252525. On adding it with 3, we have

as fraction

Hence 3.25252525….=

(d) Let x = 0.25252525

Now multiply by 100 on both the sides,

We get, 100x = 25.252525

On subtracting x from both the sides, we have

Now we have a fraction for 0.252525. On adding it with 3, we have

as fraction

Hence 3.25252525….=

### Convert the following repeating decimals to fractions

d) 3.25252525252...............

Maths-General

Complete step by step solution:

(d) Let x = 0.25252525

Now multiply by 100 on both the sides,

We get, 100x = 25.252525

On subtracting x from both the sides, we have

Now we have a fraction for 0.252525. On adding it with 3, we have

as fraction

Hence 3.25252525….=

(d) Let x = 0.25252525

Now multiply by 100 on both the sides,

We get, 100x = 25.252525

On subtracting x from both the sides, we have

Now we have a fraction for 0.252525. On adding it with 3, we have

as fraction

Hence 3.25252525….=

Maths-

### Convert the following repeating decimals to fractions

c) 0.2151515151515........

Complete step by step solution:

(c) Let x = 0.215151515…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.151515

Now multiply by 100 on both the sides in (i),

100x = 21.51515

Now multiply by 1000 on both the sides in (i),

1000x = 215.151515

On subtracting 10x from both the sides, we have

On simplification, we have

Hence 0.2151515151515....... =

(c) Let x = 0.215151515…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.151515

Now multiply by 100 on both the sides in (i),

100x = 21.51515

Now multiply by 1000 on both the sides in (i),

1000x = 215.151515

On subtracting 10x from both the sides, we have

On simplification, we have

Hence 0.2151515151515....... =

### Convert the following repeating decimals to fractions

c) 0.2151515151515........

Maths-General

Complete step by step solution:

(c) Let x = 0.215151515…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.151515

Now multiply by 100 on both the sides in (i),

100x = 21.51515

Now multiply by 1000 on both the sides in (i),

1000x = 215.151515

On subtracting 10x from both the sides, we have

On simplification, we have

Hence 0.2151515151515....... =

(c) Let x = 0.215151515…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.151515

Now multiply by 100 on both the sides in (i),

100x = 21.51515

Now multiply by 1000 on both the sides in (i),

1000x = 215.151515

On subtracting 10x from both the sides, we have

On simplification, we have

Hence 0.2151515151515....... =

Maths-

### Convert the following repeating decimals to fractions

b) 1.5555555555555

Complete step by step solution:

(b) Let x = 0.55555555

Now multiply by 10 on both the sides,

We get, 10x = 5.5555555

On subtracting x from both the sides, we have

Now we have a fraction for 0.5555555. On adding it with 1, we have

as fraction

(b) Let x = 0.55555555

Now multiply by 10 on both the sides,

We get, 10x = 5.5555555

On subtracting x from both the sides, we have

Now we have a fraction for 0.5555555. On adding it with 1, we have

as fraction

### Convert the following repeating decimals to fractions

b) 1.5555555555555

Maths-General

Complete step by step solution:

(b) Let x = 0.55555555

Now multiply by 10 on both the sides,

We get, 10x = 5.5555555

On subtracting x from both the sides, we have

Now we have a fraction for 0.5555555. On adding it with 1, we have

as fraction

(b) Let x = 0.55555555

Now multiply by 10 on both the sides,

We get, 10x = 5.5555555

On subtracting x from both the sides, we have

Now we have a fraction for 0.5555555. On adding it with 1, we have

as fraction

Maths-

### Convert the following repeating decimals to fractions

a) 1.233333333333333333

Complete step by step solution:

(a) Let x = 0.23333333…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.3333333

Now multiply by 100 on both the sides in (i),

100x = 23.3333333

On subtracting 10x from both the sides, we have

On simplification, we get

Now we have a fraction for 0.2333333…. On adding it with 1, we have

as fraction

(a) Let x = 0.23333333…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.3333333

Now multiply by 100 on both the sides in (i),

100x = 23.3333333

On subtracting 10x from both the sides, we have

On simplification, we get

Now we have a fraction for 0.2333333…. On adding it with 1, we have

as fraction

### Convert the following repeating decimals to fractions

a) 1.233333333333333333

Maths-General

Complete step by step solution:

(a) Let x = 0.23333333…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.3333333

Now multiply by 100 on both the sides in (i),

100x = 23.3333333

On subtracting 10x from both the sides, we have

On simplification, we get

Now we have a fraction for 0.2333333…. On adding it with 1, we have

as fraction

(a) Let x = 0.23333333…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.3333333

Now multiply by 100 on both the sides in (i),

100x = 23.3333333

On subtracting 10x from both the sides, we have

On simplification, we get

Now we have a fraction for 0.2333333…. On adding it with 1, we have

as fraction

Maths-

### Convert the following repeating decimals to fractions

d) 0.488888888888

Complete step by step solution:

(d) Let x = 0.4888888888

Now multiply by 10 on both the sides,

We get, 10x = 4.888888888

On subtracting from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.4888888 …. =

(d) Let x = 0.4888888888

Now multiply by 10 on both the sides,

We get, 10x = 4.888888888

On subtracting from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.4888888 …. =

### Convert the following repeating decimals to fractions

d) 0.488888888888

Maths-General

Complete step by step solution:

(d) Let x = 0.4888888888

Now multiply by 10 on both the sides,

We get, 10x = 4.888888888

On subtracting from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.4888888 …. =

(d) Let x = 0.4888888888

Now multiply by 10 on both the sides,

We get, 10x = 4.888888888

On subtracting from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.4888888 …. =

Maths-

### Convert the following repeating decimals to fractions

c) 0.366666666666

Complete step by step solution:

(c) Let x = 0.3666666

Now multiply by 10 on both the sides,

We get, 10x = 3.666666

On subtracting x from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.3666666…. =

(c) Let x = 0.3666666

Now multiply by 10 on both the sides,

We get, 10x = 3.666666

On subtracting x from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.3666666…. =

### Convert the following repeating decimals to fractions

c) 0.366666666666

Maths-General

Complete step by step solution:

(c) Let x = 0.3666666

Now multiply by 10 on both the sides,

We get, 10x = 3.666666

On subtracting x from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.3666666…. =

(c) Let x = 0.3666666

Now multiply by 10 on both the sides,

We get, 10x = 3.666666

On subtracting x from both the sides, we have

Multiply by 10 on numerator and denominator of x.

On multiplying, we have . (Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.3666666…. =

Maths-

### Convert the following repeating decimals to fractions

b) 0.155555555555

Complete step by step solution:

(b) Let x= 0.1555555555

Now multiply by 10 on both the sides,

We get, 10x = 1.55555555

On subtracting from both the sides, we have

10x - x = 1.55555555 - 0.155555555

Multiply by 10 on numerator and denominator of x.

On multiplying, we have .(Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.15555555 …. =

(b) Let x= 0.1555555555

Now multiply by 10 on both the sides,

We get, 10x = 1.55555555

On subtracting from both the sides, we have

10x - x = 1.55555555 - 0.155555555

Multiply by 10 on numerator and denominator of x.

On multiplying, we have .(Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.15555555 …. =

### Convert the following repeating decimals to fractions

b) 0.155555555555

Maths-General

Complete step by step solution:

(b) Let x= 0.1555555555

Now multiply by 10 on both the sides,

We get, 10x = 1.55555555

On subtracting from both the sides, we have

10x - x = 1.55555555 - 0.155555555

Multiply by 10 on numerator and denominator of x.

On multiplying, we have .(Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.15555555 …. =

(b) Let x= 0.1555555555

Now multiply by 10 on both the sides,

We get, 10x = 1.55555555

On subtracting from both the sides, we have

10x - x = 1.55555555 - 0.155555555

Multiply by 10 on numerator and denominator of x.

On multiplying, we have .(Since the numerator and denominator of a fraction must be integers)

On simplification, we get

Hence 0.15555555 …. =

Maths-

### Convert the following repeating decimals to fractions

a) 0.2222222

Complete step by step solution:

(a) Let x = 0.22222222…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.2222222

On subtracting x from both the sides, we have

10x - x = 2.222222 - 0.2222222

On simplification, we get

Hence 0.222222…. =

(a) Let x = 0.22222222…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.2222222

On subtracting x from both the sides, we have

10x - x = 2.222222 - 0.2222222

On simplification, we get

Hence 0.222222…. =

### Convert the following repeating decimals to fractions

a) 0.2222222

Maths-General

Complete step by step solution:

(a) Let x = 0.22222222…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.2222222

On subtracting x from both the sides, we have

10x - x = 2.222222 - 0.2222222

On simplification, we get

Hence 0.222222…. =

(a) Let x = 0.22222222…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 2.2222222

On subtracting x from both the sides, we have

10x - x = 2.222222 - 0.2222222

On simplification, we get

Hence 0.222222…. =

Maths-

### Convert 0.8363636.......as a fraction

Complete step by step solution:

Let x = 0.836363…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 8.3636363

Now multiply by 100 on both the sides in (i),

100x = 83.636363

Now multiply by 10000 on both the sides in (i),

10000x = 8363.6363

On subtracting from both the sides, we have

10000x - 100x = 8363.6363 - 83.636363

On simplification, we get x =

Hence 0.8363636..... =

Let x = 0.836363…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 8.3636363

Now multiply by 100 on both the sides in (i),

100x = 83.636363

Now multiply by 10000 on both the sides in (i),

10000x = 8363.6363

On subtracting from both the sides, we have

10000x - 100x = 8363.6363 - 83.636363

On simplification, we get x =

Hence 0.8363636..... =

### Convert 0.8363636.......as a fraction

Maths-General

Complete step by step solution:

Let x = 0.836363…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 8.3636363

Now multiply by 100 on both the sides in (i),

100x = 83.636363

Now multiply by 10000 on both the sides in (i),

10000x = 8363.6363

On subtracting from both the sides, we have

10000x - 100x = 8363.6363 - 83.636363

On simplification, we get x =

Hence 0.8363636..... =

Let x = 0.836363…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 8.3636363

Now multiply by 100 on both the sides in (i),

100x = 83.636363

Now multiply by 10000 on both the sides in (i),

10000x = 8363.6363

On subtracting from both the sides, we have

10000x - 100x = 8363.6363 - 83.636363

On simplification, we get x =

Hence 0.8363636..... =

Maths-

### Convert 17.17090090090.............. as a fraction.

Complete step by step solution:

Let x = 0.17090090…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 1.7090090

Now multiply by 100 on both the sides in (i),

100x = 17.090090

Now multiply by 1000 on both the sides in (i),

1000x = 170.90090

Now multiply by 10000 on both the sides in (i),

10000x = 1709.0090

Now multiply by 100000 on both the sides in (i),

100000x = 17090.090

On subtracting 100x from both the sides, we have

100000x - 100x = 17090.090 - 17.090090

99900x = 17073

On simplification, we get x =

Now we have a fraction for 0.17090090…. On adding it with 17, we have

as fraction

Let x = 0.17090090…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 1.7090090

Now multiply by 100 on both the sides in (i),

100x = 17.090090

Now multiply by 1000 on both the sides in (i),

1000x = 170.90090

Now multiply by 10000 on both the sides in (i),

10000x = 1709.0090

Now multiply by 100000 on both the sides in (i),

100000x = 17090.090

On subtracting 100x from both the sides, we have

100000x - 100x = 17090.090 - 17.090090

99900x = 17073

On simplification, we get x =

Now we have a fraction for 0.17090090…. On adding it with 17, we have

as fraction

### Convert 17.17090090090.............. as a fraction.

Maths-General

Complete step by step solution:

Let x = 0.17090090…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 1.7090090

Now multiply by 100 on both the sides in (i),

100x = 17.090090

Now multiply by 1000 on both the sides in (i),

1000x = 170.90090

Now multiply by 10000 on both the sides in (i),

10000x = 1709.0090

Now multiply by 100000 on both the sides in (i),

100000x = 17090.090

On subtracting 100x from both the sides, we have

100000x - 100x = 17090.090 - 17.090090

99900x = 17073

On simplification, we get x =

Now we have a fraction for 0.17090090…. On adding it with 17, we have

as fraction

Let x = 0.17090090…(i)

Now multiply by 10 on both the sides in (i),

We get, 10x = 1.7090090

Now multiply by 100 on both the sides in (i),

100x = 17.090090

Now multiply by 1000 on both the sides in (i),

1000x = 170.90090

Now multiply by 10000 on both the sides in (i),

10000x = 1709.0090

Now multiply by 100000 on both the sides in (i),

100000x = 17090.090

On subtracting 100x from both the sides, we have

100000x - 100x = 17090.090 - 17.090090

99900x = 17073

On simplification, we get x =

Now we have a fraction for 0.17090090…. On adding it with 17, we have

as fraction

Maths-

### A Manufacturer determines that the cost of making a computer the component is 2.16161616... Write the cost as a fraction and as a mixed number

Complete step by step solution:

Let x = 0.16161616

Now multiply by 100 on both the sides,

We get, 100x = 16.161616

On subtracting x from both the sides, we have

100x - x = 16.161616 - 0.16161616

Now we have a fraction for 0.161616. On adding it with 2, we have

as improper fraction

as mixed fraction

Let x = 0.16161616

Now multiply by 100 on both the sides,

We get, 100x = 16.161616

On subtracting x from both the sides, we have

100x - x = 16.161616 - 0.16161616

Now we have a fraction for 0.161616. On adding it with 2, we have

as improper fraction

as mixed fraction

### A Manufacturer determines that the cost of making a computer the component is 2.16161616... Write the cost as a fraction and as a mixed number

Maths-General

Complete step by step solution:

Let x = 0.16161616

Now multiply by 100 on both the sides,

We get, 100x = 16.161616

On subtracting x from both the sides, we have

100x - x = 16.161616 - 0.16161616

Now we have a fraction for 0.161616. On adding it with 2, we have

as improper fraction

as mixed fraction

Let x = 0.16161616

Now multiply by 100 on both the sides,

We get, 100x = 16.161616

On subtracting x from both the sides, we have

100x - x = 16.161616 - 0.16161616

Now we have a fraction for 0.161616. On adding it with 2, we have

as improper fraction

as mixed fraction

Maths-

### Write 0.87878787......... as a fraction

Complete step by step solution:

Let x = 0.87878787

Now multiply by 100 on both the sides,

We get, 100x = 87.878787

On subtracting x from both the sides, we have

100x - x = 87.878787 - 0.87878787

On simplification, we get

Hence 87878787…. =

Let x = 0.87878787

Now multiply by 100 on both the sides,

We get, 100x = 87.878787

On subtracting x from both the sides, we have

100x - x = 87.878787 - 0.87878787

On simplification, we get

Hence 87878787…. =

### Write 0.87878787......... as a fraction

Maths-General

Complete step by step solution:

Let x = 0.87878787

Now multiply by 100 on both the sides,

We get, 100x = 87.878787

On subtracting x from both the sides, we have

100x - x = 87.878787 - 0.87878787

On simplification, we get

Hence 87878787…. =

Let x = 0.87878787

Now multiply by 100 on both the sides,

We get, 100x = 87.878787

On subtracting x from both the sides, we have

100x - x = 87.878787 - 0.87878787

On simplification, we get

Hence 87878787…. =

Maths-

### Write 0. 212121.............. as a fraction

Complete step by step solution:

Let x = 0.212121

Now multiply by 100 on both the sides,

We get, 100x = 21.2121

On subtracting x from both the sides, we have

Let x = 0.212121

Now multiply by 100 on both the sides,

We get, 100x = 21.2121

On subtracting x from both the sides, we have

100x - x = 21.2121 - 0.212121

On simplification, we get

Hence 212121…. =

### Write 0. 212121.............. as a fraction

Maths-General

Complete step by step solution:

Let x = 0.212121

Now multiply by 100 on both the sides,

We get, 100x = 21.2121

On subtracting x from both the sides, we have

Let x = 0.212121

Now multiply by 100 on both the sides,

We get, 100x = 21.2121

On subtracting x from both the sides, we have

100x - x = 21.2121 - 0.212121

On simplification, we get

Hence 212121…. =