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 100x = 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 100x = 23.23 = 23 + 23, so 100x = 23 + x. This gives us an equation we can solve to find x. Subtracting x from both sides gives 99x = 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:
In the following problems it is not necessary to reduce the fractions to lowest terms.
Problem 2. Convert the following decimals to fractions:
Problem 3. Convert the following repeating decimals to fractions:
Problem 4. Convert the following repeating decimals to fractions: