This tutorial is provided as supplementarymaterial for courses taught at Howard Community College, and in this tutorial I'm going to talk aboutterminating and repeating decimals. So you may have noticed that sometimes when you've got a fraction, like the fraction 3 over 11, and you turn that into a decimal,
you get what's called repeating decimal. When we turn 3 over 11 into a decimalwe get 0.27 2727. And this repeating pattern, the 27, is going to keep on going. So I'm just going to write
an ellipsis, three dots, to show that it keeps going. Sometimes you'll see this written as 0 point 27 and bar over the digits that repeat. So a bar over27 to show that this goes on infinitely.
Now other times you might divide afraction, you might have a fraction like 7 over 8, and when you turn that into a decimal you end up with what's called terminating decimal. So 7 over 8 is going to turn into 0.875. Now there's a general rule of thumb that tells you whether you're going toend up with repeating decimal
or a terminating decimal. The rule goes like this: take your fraction and reduce it to lowestterms. Once it's reduced to lowest terms, factor the denominator. If the denominator has no prime factors other than 2 and 5, you're gong to have a terminatingdecimal. In other words, if all you have is
2's and 5's, then you'll get a terminating decimal. Otherwise you'll get a repeating decimal. So let's look at some fractions andsee whether they'll terminate or repeat. So if I have the fraction 3 over 16, it's reduced as much as possible. I'll factor the denominator,