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24 July, 01:19

What is 2.1 with the one repeating as a fraction? with work if possible

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Answers (1)
  1. 24 July, 01:44
    0
    2.1¯¯¯=219

    2.

    1

    ¯

    =

    2

    1

    9

    Showing the work

    Let X equal our decimal number (fraction)

    Equation 1:

    X=2.1¯¯¯ (1)

    (1) X=2.

    1

    ¯

    Since we have 1 digits in our repeating decimal

    group, create a second equation by multiplying

    both sides by 101 = 10

    Equation 2:

    10X=21.1¯¯¯ (2)

    (2) 10X=21.

    1

    ¯

    Subtracting equation (1) from (2)

    10XX9X===21.1 ... 2.1 ... 19

    10X = 21.1 ... X = 2.1 ... 9X = 19

    We get

    9X=19

    9

    X

    =

    19

    Solving for X

    X=199

    X

    =

    19

    9

    Simplifying the improper fraction,

    =219

    =

    2

    1

    9

    In conclusion,

    2.1¯¯¯=219

    2.

    1

    ¯

    =

    2

    1/9
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