How do you convert 3.142 (142 repeating) as a fraction?

Question

3593 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-10T22:38:25

#3.bar(142) = 3139/999#

Multiply by #1000-1# to shift the number three places to the left and subtract the original to eliminate the repeating decimal tail...

#(1000-1)*3.bar(142) = 3142.bar(142) - 3.bar(142) = 3139#

Dividing both sides by #(1000-1)# we find:

#3.bar(142) = 3139 / (1000-1) = 3139/999#

This improper fraction is in lowest terms, since:

#3139 = 43 * 73#

#999 = 3*3*3*37#

So #3139# and #999# have no common factors larger than #1#.