How do you convert 730.4810 (10 being repeated) to a fraction?

1 Answer
Feb 24, 2016

#730.48bar10 = 730color(white)(.) 4762/9900#

Explanation:

There is a clever trick to do this

The bar means repeats for ever (dots are sometimes used)
Let #x=0.48bar10#

So #" "100x=48.10bar10#

and#" "10000x=4810.bar10#

#10000x-100x=4810.bar10 - 48.bar10#

#9900x=4762#

So#" "x=4762/9900#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus: #730.48bar10 = 730color(white)(.) 4762/9900#

#color(brown)("It is all a matter of spotting how to multiply up the values so that the")##color(brown)("subtraction removes the repeating decimal part.")#