Express the number five-sixths as a decimal.
This question is asking us to take a fraction and turn it into a decimal. To do that, we’ll need to divide the numerator by the denominator. In this case, we’ll divide five by six. We first ask, how many times does six go into five? Six goes into five zero times. Zero times six equals zero; five minus zero equals five. In order to continue dividing, we’ll need to add a decimal and then a zero to the right of the decimal. We bring that zero down and then we ask the question, how many times does six go into fifty? The answer is eight times. Six times eight equals forty-eight; fifty minus forty-eight equals two.
We still have a remainder here, so we’ll bring an additional zero down. And then we’ll say, how many times is twenty divided by six? The answer is three times. Six times three equals eighteen; twenty minus eighteen equals two. At this point, we can add another zero. And we’re asking the question, how many times is six divided into twenty? That’s the same answer: three times. Three times six equals eighteen. And again, we have a remainder of two.
If I add another zero here, we’re going to ask the same question again, how many times does six go into twenty? Notice how we’re having this two appear again and again; notice how we have this repetition of twenty or remainder two in our division. This is important; it tells us that we’re going to have a recurring decimal. This is a decimal that doesn’t terminate; it doesn’t have an end. No matter how many times we added a zero to the end of our decimal, we’re going to continue to get three, three, three, three, three. We call this a recurring decimal because it doesn’t terminate; there is no end.
When we have a recurring decimal, we use a special notation; it looks like this. This bar on the top of the three tells us that that three is repeating over and over and over again. If we wanna write five-sixths as a decimal, we write zero decimal eight three with a bar over the top. The bar just goes over the three because only the three is the repeating portion. Our final answer is zero decimal eight three repeating.