How do you convert 0.63 (63 being repeated) to a fraction?

Question

104907 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-16T04:14:31

#7/11#

We let 0.63 (63 being repeated) be #x#.

#x = 0.6363...#

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

#100x = 63.6363...#

Next, we subtract them.

#100x - x = 63.6363... - 0.6363...#

#99x = 63#

The recurring digits '63' cancel off and the result is that #99x# is non-recurring.

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

#x = 63/99#

#= 7/11#

Therefore,

#0.6363... = 7/11#