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    Converting decimal to fraction

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    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Find the fraction 1.14232323

    Please help explain the process.

    © BrainMass Inc. brainmass.com September 29, 2022, 2:15 pm ad1c9bdddf
    https://brainmass.com/math/fractions-and-percentages/converting-decimal-fraction-178903

    SOLUTION This solution is FREE courtesy of BrainMass!

    This will help to analyze decimals to fractions:
    -----------------------------------------------------------------------------------------------------
    Note the following pattern for repeating decimals:
    0.22222222... = 2/9
    0.54545454... = 54/99
    0.298298298... = 298/999
    Division by 9's causes the repeating pattern.

    Note the pattern if zeros precede the repeating decimal:
    0.022222222... = 2/90
    0.00054545454... = 54/99000
    0.00298298298... = 298/99900
    Adding zero's to the denominator adds zero's before the repeating decimal.
    --------------------------------------------------------------------------------------------------------

    Now onto this problem!

    To convert a decimal that begins with a non-repeating part, such as 1.14232323..., to a fraction, write it as the sum of the non-repeating part and the repeating part.

    1 + 0.14 + 0.00232323...

    Next, convert each of these decimals to fractions. The first is just 1. The second is a decimal and has a divisor of power ten. The third decimal (which repeats) is converted according to the pattern above.

    1 + 14/100 + 23/9900

    Now add these fraction by expressing both with a common divisor

    9900/9900 + 1386/9900 + 23/9900

    and add

    11309/9900

    and check on your calculator or with long division.

    = 1.14232323...

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com September 29, 2022, 2:15 pm ad1c9bdddf>
    https://brainmass.com/math/fractions-and-percentages/converting-decimal-fraction-178903

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