Decimal to Fraction

Step 9: Decimal numbers to mixed fractions

If you happen to start with a number in decimal form, this process of finding a mixed fraction is much, much, easier.

With a number in decimal form, you can find the integer part and the proper fraction part, essentially from inspection. All the digits to the left of the decimal point represent an integer, and all the digits to the right of the decimal point represent a proper fraction.

3.125 = 3 + 0.125

By the way, concerning this number formed from only the digits to right side of the decimal point, we know it represents a proper fraction because it has to be less than 1.

0.125 represents a proper fraction since 0.125 < 1

Now, I know what some of you are thinking. You're thinking:

"Dammit, Jack! What about all those previous examples where I started out with a decimal number with a non-zero integer part? Couldn't I have just subtracted out the integer part first? Like 3.125? Wouldn't it simplify things considerably to subtract out the 3 first?"

Yeah, sure. That's cool ese. You could definitely do it that way.In fact, subtracting out the integer part first will be especially helpful if a mixed fraction is the form you are working towards.

For example, let us re-examine:

r = 3.125

This time, write it as the sum of its integer part and its fractional part.

r = 3 + 0.125 = 3 + 125/1000 = 3 + 1/8

And there's your answer, in the form of a mixed fraction.