How do you simplify and make the fraction 16/88 into a decimal?

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Answer 1 · 2015-10-01T22:46:18

To simplify, factor the numerator and denominator to find the greatest common factor $8$ $8$ and divide both by that to find:

$\frac{16}{88} = \frac{2}{11}$ $16/88 = 2 / 11$

Then find $\frac{2}{11} = 0 . . 1 . 8$ $2/11 = 0.dot(1)dot(8)$

$16 = 2 \cdot 8$ $16 = 2 * 8$ and $88 = 11 \cdot 8$ $88 = 11 * 8$

So:

$\frac{16}{88} = \frac{2 \cdot 8}{11 \cdot 8} = \frac{2}{11} \cdot \frac{8}{8} = \frac{2}{11}$ $16/88 = (2*8)/(11*8) = 2/11 * 8/8 = 2/11$

To convert $\frac{2}{11}$ $2/11$ to a decimal we can long divide and recognise the repetition of the remainder...

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Notice that after a couple of digits we're back to the number $2$ $2$ we first started with. So $2/11 = 0.18181818... = 0.dot(1)dot(8)$

Alternatively, just notice that $9 xx 11 = 99$ , so

$2/11 = 2/11 * 9/9 = 18/99 = 0.dot(1)dot(8)$