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

Question

1462 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-01T22:46:18

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

#16/88 = 2 / 11#

Then find #2/11 = 0.dot(1)dot(8)#

#16 = 2 * 8# and #88 = 11 * 8#

So:

#16/88 = (2*8)/(11*8) = 2/11 * 8/8 = 2/11#

To convert #2/11# to a decimal we can long divide and recognise the repetition of the remainder...

enter image source here

Notice that after a couple of digits we're back to the number #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)#