Question

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

Answer 1

`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.")`