How do you convert #0.bar(15)# (15 being repeated) to a fraction?

Question

27046 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-18T03:50:13

#5/33#

We first let #0.bar(15)# (15 being repeated) be #x#.

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

#" "x = 0.151515....#
#100x = 15.151515...#

Next, we subtract them.

#100x - x = 15.151515 - 0.151515#

#99x = 15#

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

#x = 15/99#

#= 5/33#