# Decimals to Fractions

• Jul 21st 2010, 11:43 AM
David Green
Decimals to Fractions
Hi All,

My basic maths are not the best on the planet in some areas, would somebody be able to advice how to change decimals to fractions and vica versa?

Example;

convert 13mm to a fraction?

Convert 13/15 to a decimal?

13/15 = 0.86, but what would I do to change the decimal to a fraction?

Any help much appreciated
• Jul 21st 2010, 12:44 PM
eumyang
Actually, 13/15 = 0.86666666.., a non-terminating, repeating decimal.

Here's a way to convert this decimal to a fraction. Let's assign a variable to this decimal:

$N = 0.866666666...$

Multiply both sides of this by 100 and 10:

\begin{aligned}
100N &= 86.666666666... \\
10N &= 8.666666666...
\end{aligned}

Subtract the 2nd line from the first:
$90N = 78$

Divide both sides by 90 to solve for N:
$N = \frac{78}{90} = \frac{13]{15}$
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