OK, OK, OK!  Wait a minute here!  How on earth did I know to multiply that guy by 125?!

Heh, heh...  Because I'm smart!  Alright, I'll tell you how I knew.

I know that I want that denominator to be 10 or 100 or 1000 or 10,000... a power of 10...  And 10's are made up of 2's and 5's:

powers of 10's and their equivalent "2 and 5" pairs

So, we need a PAIR of 2's and 5's!

Look at this guy:


fraction to decimal conversion example

Here's another one:


fraction to decimal conversion example

Note that this will ONLY work if your denominator is made up of nothing but 2's and/or 5's.

Can you convert  7/75 this way?

fraction example

But, there will be another way...  There will be another way.