## 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:

[img id:7822]

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.

*Read it*: .8 (eight tenths)

*Write it*: 8/10

*Reduce it*: 4/5

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

*Read it:* .09 (nine hundredths)

*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 10*n* 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