Learning Competencies

To convert fractions to decimals, look at the fraction as a division problem. Take the top number, or the numerator, of the fraction and divide it by the bottom number, or the denominator. You can do this in your head, by using a calculator, or by doing long division. For example, ¼ is just 1 divided by 4, or 0.25.

• To change terminating decimals to fractions, simply remember that all numbers to the right of the decimal point are fractions with denominators of only 10, 100, 1,000, 10,000, and so on. Next, use the technique of read it,write it, and reduce it (that is, simplify).

In the case of a repeating decimal, the following procedure is often used. Suppose you have a number like 0.5777777.... This number is equal to some fraction; call this fraction "x". That is:

x = 0.5777777...

There is one repeating digit in this decimal, so multiply x by "1" followed by one zero; that is, multiply by 10:

10x = 5.777777...

Now subtract the former from the latter:

10x = 5.777777...

x = 0.5777777...

9x = 5.777777...

That is, 9x = 5.2 = 52/10 =26/5. Solving this, (by dividing through by 9), we get x = 26/5