## How do you convert a fraction to a decimal or change a decimal to a fraction?

Fractions can be hard, but I use them almost every day; for example, if I eat 5/8ths of a whole pizza for dinner, how much will I have left over for lunch the next day? (My cooking skills aren't that hot.)

Fractions can also appear in decimal form. These decimal fractions come in two styles: terminating decimals (for example, .3) and infinite repeating decimals (for example, .66 . . .).

To change a fraction to a decimal, simply do what the operation says. In other words, 5/8 means 5 divided by 8. Don't forget to insert the decimal points and zeros when you do the division!

Change 5/8 into a decimal:

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So 5/8 = .625 (Now that's a lot of pizza!)

To change terminating decimals to fractions, 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.

(a) Change .8 to a fraction in lowest terms.

Write it: 8/10

Reduce it: 4/5

(b) Change .09 to a fraction in lowest terms.

Write it: 9/100

Reduce it: 9/100 Can't be reduced

To change an infinite repeating decimal to a fraction, remember that every infinite repeating decimal can be expressed as a fraction. Infinite repeating decimals are usually represented by putting a line over (sometimes under) the shortest block of repeating decimals.

Find the fraction represented by the repeating decimal .7

Let n stand for .7 or .77777 . . .

So 10n stands for 7.7 or 7.77777 . . .

10n and n have the same fractional part, so their difference is an integer.

10n = 7.7 - n = .7 ---------- 9n = 7

Solve this problem as follows.

9n = 7 n = 7/9 .7 = 7/9