Math CentralQuandaries & Queries


Question from Preitty, a student:

How can I turn fractions into percentages when the denominator is not a number that can multiply to 100?


Suppose we look at $\large \frac2{7}$ and we want to express this fraction as a percentage. Thus we want to find $x$ if

\[\frac27 = \frac{x}{100}.\]

Clearly $x$ is not an integer since 100 is not a multiple of 7 but you can still solve for $x.$ Multiply both sides of the equation above by 100 to get

\[100 \times \frac27 = x\]


\[x = 100 \times \frac27 = 100 \times 0.285714285714\]

where the pattern "285714" is a repeating. The way you express $x$ depends on the situation. It may be good enough to say $x = 29\%$ or you might want to express $x$ with two decimal place accuracy so you have $x = 28.57\%$ or you might want some other level of accuracy.

I hope this helps,

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