In this lesson we're going to learn how to convert decimals into fractions. Now, depending on the size of our decimal, that's going to determine what kind of fraction we'll end up with. So if the decimal is less than one, it will become a proper fraction. And that's where the numerator is smaller than the denominator. Decimals that are more than one will become either improper fractions where the numerator is larger than the denominator, or we can also write them as mixed fractions where we have the whole number part and the fraction part. For our first example, we'll write 0.9 as a fraction. Looking at that decimal 0.9, we can see that it's less than one. So we can expect that our fraction will be a proper fraction where the numerator is smaller than the denominator. So first we'll draw our fraction line. And now we just need to see what numbers go above and below it. So we'll use the numbers after the decimal point as the numerator. The only number that we have after our decimal point is the nine. So we'll write that as our numerator. Now, to find the denominator, we'll look at the place value of the last digit and whatever place value it's in will determine what the denominator of our fraction is. Our last digit is nine and it's in the 10th place. So that means our denominator will be ten. And now our fraction is complete and we can see that it is a proper fraction because the numerator nine is smaller than the denominator of ten. We could also read this fraction as nine tenths. Here's our next example. Write 6.301 as an improper fraction. Notice this number is greater than one. We have 6.301. So we could write it as an improper fraction or a mixed fraction. But first we'll see what it looks like as an improper fraction. So we set up our fraction line. And first we'll remove the decimal point from our number and use the numbers as the numerator of the fraction. So we just have the 6301 but no decimal point there. And now we'll do just like before to look at the last digit’s place value and use that to figure out what the denominator will be. Our last digit is the one and it's in the thousandths place. So our fraction has a denominator of 1000. So putting this together, we can read it as 6,301 thousandths. And looking at our fraction, it's an improper fraction because the numerator of 6301 is larger than the denominator of 1000. Now let's look how we can write that same number, 6.301, but as a mixed fraction. So we'll start off with our same number. We have our fraction line, but we're also going to have a whole number in front of that fraction. So whatever numbers are to the left of the decimal point, that will become the whole number part of our mixed fraction. So we only have a six that's to the left of our decimal point. So our whole number part is six. Then we use the numbers after the decimal point as the numerator so that's the 301, place that up top is the numerator. And just like with our other examples we look to the last digit’s place value to determine the denominator. So that last digit is a one which is in the thousandths place. So our denominator once again is 1000. So we can see we have a mixed fraction because we have the whole number part which is the six and we have the fraction next to it which is the 301 over 1000. So we can read that as six and 301 thousandths.