Maths-
General
Easy

Question

Convert the following fractions to repeating decimals
c) 10 over 33

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

    General
    Maths-

    Convert the following fractions to repeating decimals
    b) 7 over 18

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

    Convert the following fractions to repeating decimals
    b) 7 over 18

    Maths-General
    Complete step by step solution:
    (b) On dividing 7 by 18, we have 0.3888888888.. as the corresponding decimal number.
    General
    Maths-

    Convert the following fractions to repeating decimals
    a) 11 over 12

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

    Convert the following fractions to repeating decimals
    a) 11 over 12

    Maths-General
    Complete step by step solution:
    (a) On dividing 11 by 12, we have 0.9166666666.. as the corresponding decimal number.
    General
    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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 100 x minus x equals 25.252525 minus 0.25252525 end cell row cell not stretchy rightwards double arrow 99 x equals 25 end cell row cell not stretchy rightwards double arrow x equals 25 over 99 end cell end table
    Now we have a fraction for 0.252525. On adding it with 3, we have
    rightwards double arrow 3 space plus space 25 over 99
    rightwards double arrow 322 over 99 as fraction
    Hence 3.25252525….= 322 over 99

    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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 100 x minus x equals 25.252525 minus 0.25252525 end cell row cell not stretchy rightwards double arrow 99 x equals 25 end cell row cell not stretchy rightwards double arrow x equals 25 over 99 end cell end table
    Now we have a fraction for 0.252525. On adding it with 3, we have
    rightwards double arrow 3 space plus space 25 over 99
    rightwards double arrow 322 over 99 as fraction
    Hence 3.25252525….= 322 over 99
    parallel
    General
    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
    1000 x minus 10 x equals 215.1515 minus 2.151515
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 990 x equals 213 end cell row cell not stretchy rightwards double arrow x equals 213 over 990 end cell end table
    On simplification, we have x equals 71 over 330
    Hence 0.2151515151515....... = 71 over 330

    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
    1000 x minus 10 x equals 215.1515 minus 2.151515
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 990 x equals 213 end cell row cell not stretchy rightwards double arrow x equals 213 over 990 end cell end table
    On simplification, we have x equals 71 over 330
    Hence 0.2151515151515....... = 71 over 330
    General
    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
    table attributes columnspacing 1em end attributes row cell 10 x minus x equals 5.55555555 minus 0.555555555 end cell row cell not stretchy rightwards double arrow 9 x equals 5 end cell row cell not stretchy rightwards double arrow x equals 5 over 9 end cell end table
    Now we have a fraction for 0.5555555. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 5 over 9
    not stretchy rightwards double arrow 14 over 9as 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
    table attributes columnspacing 1em end attributes row cell 10 x minus x equals 5.55555555 minus 0.555555555 end cell row cell not stretchy rightwards double arrow 9 x equals 5 end cell row cell not stretchy rightwards double arrow x equals 5 over 9 end cell end table
    Now we have a fraction for 0.5555555. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 5 over 9
    not stretchy rightwards double arrow 14 over 9as fraction
    General
    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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 100 x minus 10 x equals 23.3333 minus 2.3333333 end cell row cell not stretchy rightwards double arrow 90 x equals 21 end cell row cell not stretchy rightwards double arrow x equals 21 over 90 end cell end table
    On simplification, we get x equals 7 over 30
    Now we have a fraction for 0.2333333…. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 7 over 30
    not stretchy rightwards double arrow 37 over 30 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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 100 x minus 10 x equals 23.3333 minus 2.3333333 end cell row cell not stretchy rightwards double arrow 90 x equals 21 end cell row cell not stretchy rightwards double arrow x equals 21 over 90 end cell end table
    On simplification, we get x equals 7 over 30
    Now we have a fraction for 0.2333333…. On adding it with 1, we have
    not stretchy rightwards double arrow 1 plus 7 over 30
    not stretchy rightwards double arrow 37 over 30 as fraction
    parallel
    General
    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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 10 x minus x equals 4.88888888 minus 0.48888888 end cell row cell not stretchy rightwards double arrow 9 x equals 4.4 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 4.4 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have 22 over 45. (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 22 over 45
    Hence 0.4888888 …. = 22 over 45
     

    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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 10 x minus x equals 4.88888888 minus 0.48888888 end cell row cell not stretchy rightwards double arrow 9 x equals 4.4 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 4.4 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have 22 over 45. (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 22 over 45
    Hence 0.4888888 …. = 22 over 45
     
    General
    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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 10 x minus x equals 3.666666 minus 0.3666666 end cell row cell not stretchy rightwards double arrow 9 x equals 3.3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 3.3 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have .11 over 30 (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 11 over 30
    Hence 0.3666666…. = 11 over 30
     

    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
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 10 x minus x equals 3.666666 minus 0.3666666 end cell row cell not stretchy rightwards double arrow 9 x equals 3.3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 3.3 over denominator 9 end fraction end cell end table
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have .11 over 30 (Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 11 over 30
    Hence 0.3666666…. = 11 over 30
     
    General
    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
    rightwards double arrow 9 x space equals space 1.4
rightwards double arrow x space equals space fraction numerator 1.4 over denominator 9 end fraction
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have 14 over 90.(Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 7 over 45
    Hence 0.15555555 …. = 7 over 45

    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
    rightwards double arrow 9 x space equals space 1.4
rightwards double arrow x space equals space fraction numerator 1.4 over denominator 9 end fraction
    Multiply by 10 on numerator and denominator of x.
    On multiplying, we have 14 over 90.(Since the numerator and denominator of a fraction must be integers)
    On simplification, we get 7 over 45
    Hence 0.15555555 …. = 7 over 45
    parallel
    General
    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
    rightwards double arrow 9 x space equals space 2
rightwards double arrow x space equals space 2 over 9
    On simplification, we get 2 over 9
    Hence 0.222222…. = 2 over 9

    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
    rightwards double arrow 9 x space equals space 2
rightwards double arrow x space equals space 2 over 9
    On simplification, we get 2 over 9
    Hence 0.222222…. = 2 over 9
    General
    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
    rightwards double arrow 9900 x space equals space 8280
rightwards double arrow x space equals space 8280 over 9900
    On simplification, we get x = 46 over 55
    Hence 0.8363636..... = 46 over 55

    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
    rightwards double arrow 9900 x space equals space 8280
rightwards double arrow x space equals space 8280 over 9900
    On simplification, we get x = 46 over 55
    Hence 0.8363636..... = 46 over 55
    General
    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
    rightwards double arrow99900x = 17073
    rightwards double arrow x space equals space 17073 over 99900
    On simplification, we get x = 1897 over 11100
    Now we have a fraction for 0.17090090…. On adding it with 17, we have
    rightwards double arrow 17 space plus space 1897 over 11100
    rightwards double arrow 190597 over 11100 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
    rightwards double arrow99900x = 17073
    rightwards double arrow x space equals space 17073 over 99900
    On simplification, we get x = 1897 over 11100
    Now we have a fraction for 0.17090090…. On adding it with 17, we have
    rightwards double arrow 17 space plus space 1897 over 11100
    rightwards double arrow 190597 over 11100 as fraction
    parallel
    General
    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
    rightwards double arrow 99 x space equals space 16
rightwards double arrow x space equals space 16 over 99
    Now we have a fraction for 0.161616. On adding it with 2, we have
    not stretchy rightwards double arrow 2 plus 16 over 99
    not stretchy rightwards double arrow 214 over 99 as improper fraction
    not stretchy rightwards double arrow 2 16 over 99 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
    rightwards double arrow 99 x space equals space 16
rightwards double arrow x space equals space 16 over 99
    Now we have a fraction for 0.161616. On adding it with 2, we have
    not stretchy rightwards double arrow 2 plus 16 over 99
    not stretchy rightwards double arrow 214 over 99 as improper fraction
    not stretchy rightwards double arrow 2 16 over 99 as mixed fraction
    General
    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
    rightwards double arrow 99 x space equals space 87
rightwards double arrow x space equals space 87 over 99
    On simplification, we get 29 over 33
    Hence 87878787…. = 29 over 33

    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
    rightwards double arrow 99 x space equals space 87
rightwards double arrow x space equals space 87 over 99
    On simplification, we get 29 over 33
    Hence 87878787…. = 29 over 33
    General
    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

    100x - x = 21.2121 - 0.212121
    rightwards double arrow 99 x space equals space 21
rightwards double arrow x space equals space 21 over 99
    On simplification, we get 7 over 33
    Hence 212121…. = 7 over 33

    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

    100x - x = 21.2121 - 0.212121
    rightwards double arrow 99 x space equals space 21
rightwards double arrow x space equals space 21 over 99
    On simplification, we get 7 over 33
    Hence 212121…. = 7 over 33

    parallel

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