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The procedure depends on whether the decimal is terminating or recurring.

Terminating decimal

  • Count the number of digits after the decimal point. Suppose this number is d.
  • Write the given decimal, without the decimal point, as the numerator of the fraction.
  • Write 1 followed by d zeros as the denominator of the fraction.
  • Simplify, if required and if possible.

For example,

If you have 5.679, then d = 3

So the fraction is 5679/1000 which cannot be simplified.

Recurring decimal

  • This is not quite as simple. Write f = fraction.
  • Count the length of the string that repeats (s).
  • Calculate f*10^s, that is f time the number which is 1 followed by s zeros.
  • Subtract the first equation from the second, solve and simplify, if possible.

For example,

Suppose f 1.4636363... with the string "63" repeating. Therefore s = 2

So 100f = 146.3636363...

Subtracting gives 99f = 144.9

And so f = 144.9/99 = 1449/990 = 161/110.

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9y ago
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8y ago

Say it out loud 0.37 = thirty-seven hundredths = 37/100

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Q: How do you make a decimal into a fraction easy?
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