Basic Math and Pre-Algebra For Dummies (59 page)

In the following sections, I show you how to convert decimals to fractions when you have to work with mixed numbers and reduce the terms.

When you convert a decimal greater than 1 to a fraction, the result is a mixed number. Fortunately, this process is easy because the whole number part is unaffected by the conversion. So focusing only on the decimal part, follow the same steps I outline in the preceding section.

For example, suppose you want to change 4.51 to a fraction. The result will be a mixed number with a whole number part of 4. To find the fractional part, follow these steps:

1. Draw a line (fraction bar) under the decimal and place a 1 underneath it.
   

   Draw a line under 0.51 and place a 1 underneath it:
   

   

2. Move the decimal point one place to the right and add a 0 after the 1.
   

   

3. Repeat Step 2 until the decimal point moves all the way to the right so you can drop the decimal point entirely.
   

   In this case, you have only one additional step:
   

   

So the mixed-number equivalent of 4.51 is
.

Converting fractions to decimals isn't difficult, but to do it, you need to know about decimal division. If you need to get up to speed on this, check out “Dividing decimals,” earlier in this chapter.

 To convert a fraction to a decimal, follow these steps:

1. Set up the fraction as a decimal division, dividing the numerator (top number) by the denominator (bottom number).
   
2. Attach enough trailing zeros to the numerator so that you can continue dividing until you find that the answer is either a
   terminating decimal
   or a
   repeating decimal.
   

Don't worry, I explain terminating and repeating decimals later.

Sometimes when you divide the numerator of a fraction by the denominator, the division eventually works out evenly. The result is a
terminating decimal.

For example, suppose you want to change the fraction
to a decimal. Here's your first step:

One glance at this problem, and it looks like you're doomed from the start because 5 doesn't go into 2. But watch what happens when I add a few trailing zeros. Notice that I also place another decimal point in the answer just above the first decimal point. This step is important — you can read more about it in “Dividing decimals”:

Now you can divide because, although 5 doesn't go into 2, 5 does go into 20 four times:

You're done! As it turns out, you needed only one trailing zero, so you can ignore the rest:

Because the division worked out evenly, the answer is an example of a
terminating decimal.

As another example, suppose you want to find out how to represent
as a decimal. As earlier, I attach three trailing zeros: