How do you convert 0.809 (09 being repeated) to a fraction?

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Answer 1 · 2016-03-16T04:40:15

#89/110#

We first let 0.809 (09 being repeated) be #x#.

Since #x# is recurring in 2 decimal places, we multiply it by 100.

#100x = 80.909#

Next, we subtract them.

#100x - x = 80.909 - 0.809#

#99x = 80.1#

Lastly, we divide both sides by 99 to get #x# as a fraction.

#x = 80.1/99#

#= 801/990#

#= 89/110#