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Question

Although I understand how to convert a decimal such as .33 into a fraction, how do I convert a decimal such as 1.3333 into a fraction?

One method to convert a decimal directly into a fraction is to place the number to the right of the decimal over a power of 10. Which power of 10 you use depends on how many digits there are to the right of the decimal. So for example:

0.5 ==> 5 is to the right of the decimal, and is only 1 digit so we have:

5/10

Now reduce (divide both the top and bottom by their greatest common divisor—5 in this case—to get:

1/2

Let's try a different number:

0.25 ==> 25 is to the right of the decimal, so that's 2 digits:

25/100

Now reduce to get:

1/4

Now, notice that there are an equal number of 0s after the 1 in the denominator as there are digits after the decimal (25 is two digits, so the denominator is 100 [two 0s]). Again, those are very basic ones that you'd be expected to know immediately.

So to complicate things a bit further, what happens if you're faced with something like 2.75? Well simply separate it into 2 + 0.75:

2 + 0.75

2 + 75/100

2 + 3/4

8/4 + 3/4 ==> note that 1 = 4/4, that way we can have the same denominator.

11/4

OR, very similarly, we can convert into a mixed number, then convert that into a fraction. We do:

2 + 0.75 =

2 3/4 =

(4 * 2 + 3) / 4 =

11/4

We discuss converting mixed numbers into fractions in the intro to fractions lesson.

OR (yet another method) you don't have to separate. Say you have 14.45 You can still:

1) Move the decimal to right "x" times until you have a whole number. So for 14.45, you move the decimal 2 times to the right to get 1445

2) Put the whole number over 10 to the power of x. In other words, a 1 with one zero for each time you moved the decimal. In this examples, we moved the decimal 2 times, so we put 1445 over 10^2 or 100.

3) Now just reduce the fraction 1445/100 (find the greatest common divisor and divide) In this case, the greatest common divisor is 5, and we get 289/20.

For 2.75, we would have:

1) 2.75 ==> 275/100

2) Reduce -- the greatest common divisor is 25, so we have:

11/4 again

If you want to review finding the greatest common divisor, it's here:

greatest common divisor

In general, we recommend that you memorize the conversions for most of the basic fractions, particularly:

1/2 = 0.5

1/3 = 0.33 (repeating)

1/4 = 0.25

1/5 = 0.2

1/6 = 0.166 (repeating)

Note: If the decimal is repeating, just as 1.33333 (repeating) or 216666 (repeating), then we can't directly use the last approach (the one without separation above; It's better to recognize what fraction the repeating part is and use one of the separation methods.