If you have a rational number written as a fraction, you get the decimal representation by long division. To convert from terminating decimals to fractions is quick if you remember what decimals represent. For example, .7 means 7 tenths, so .7 = 7/10. Also, .63 means 63 hundredths, so .63 = 63/100. Alternatively, if *x* = .63, then 100*x* = 63, so *x* = 63/100.

For repeating decimals, the process is a little more involved, but basically uses the same ideas. Here is an example. Suppose we want to convert .232323^{ . . .} to a fraction. Call this number *x*. If we multiply *x* by 100, we get 100*x* = 23.23 = 23 + 23, so 100*x* = 23 + *x*. This gives us an equation we can solve to find *x*. Subtracting *x* from both sides gives 99*x* = 23, so *x* = 23/99. The reason we multiplied *x* by 100 is because we had two repeating digits. If we had three repeating digits, we would multiply by 1000.

**Problem 1.** Convert the following fractions to decimals:

- 15/8
- 7/11
- 2/7

In the following problems it is not necessary to reduce the fractions to lowest terms.

**Problem 2.** Convert the following decimals to fractions:

- .35
- 2.461
- 3.13432

**Problem 3.** Convert the following repeating decimals to fractions:

- .7
- .32
- .432

**Problem 4.** Convert the following repeating decimals to fractions:

- 1.5
- .23
- -3.2178