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# Converting decimal to fraction

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Find the fraction 1.14232323

© 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:
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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.
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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