How do you convert 0.345 (345 being repeated) to a fraction?

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Answer 1 · 2016-03-17T04:59:57

#115/333#

We first let 0.345 (345 being repeated) be #x#.

Since #x# is recurring in 3 decimal places, we multiply it by 1000.

#1000x = 345.345#

Next, we subtract them.

#1000x - x = 345.345 - 0.345#

#999x = 345#

Lastly, we divide both sides by 999 to get #x# as a fraction.

#x = 345/999#

#= 115/333#