How to Convert a Fraction to a Decimal | Math with Mr. J

Welcome to Math with Mr. J. In this video, I'm going to cover how to convert fractions to decimals. We will go through four examples. For numbers one and two, we will work through them by hand, so without a calculator. And then numbers three and four, we will work through those by discussing what we need to plug into a calculator. Let's jump into number one, where we have one eighth. Now, when we convert a fraction to a decimal, we can divide the numerator, the top number of the fraction, by the denominator, the bottom number of the fraction. So for number one, we need to do one divided by eight. So let's set this up. One divided by eight. Now, as far as one divided by eight, how many whole groups of eight in one? How many eights in one? Well, we can't do that. So we need to use a decimal and then a zero in order to work through the division. Remember, zeros to the right of a decimal or decimal digits do not change the value of the number. So we're able to do this. Now, once we have that decimal and the zero, we can bring the decimal straight up into the quotient, the answer. And I'm going to extend the division bar as well. Now, we can think of this as 10 divided by eight. So how many whole groups of eight in 10? How many eights in 10? Well, one. So we need to put the one above the zero. Now, make sure that one is above the zero, not the one. We used that zero in the tenths place and thought of this as 10. So the one needs to go above that zero in order to keep everything lined up correctly. Now, we multiply one times eight, eight. Subtract 10 minus eight is two. Now, we don't have a clean cut zero there at the bottom. So what we can do, we can use another zero that we can bring down to continue on. Now, we have 20, 20 divided by eight. So how many whole groups of eight in 20? Well, two. That gets us to 16. Two times eight, 16. Subtract 20 minus 16 is four. So we still don't have that clean cut zero there at the bottom. So let's use another zero that we can bring down. So now we have 40, 40 divided by eight. How many whole groups of eight in 40? Well, five. And that hits 40 exactly. Five times eight is 40. Subtract 40 minus 40 is zero. So now we have that clean cut zero there at the bottom. We went all the way over within our division problem and we have that zero at the bottom. So we are done. We get .125, 125 thousandths. 1 8th equals 0.125. So 125 thousandths. Now you'll notice when I rewrote that decimal, I started with a zero and then the decimal. This is common when writing decimals because it helps us recognize and see the decimal. We don't want the decimal to get overlooked. So something to keep in mind. Let's move on to number two where we have 5 12ths. So we need to do five divided by 12. So let's set this up. We have five divided by 12. So five divided by 12. How many whole groups of 12 in five? Well, we can't do that. So we need a decimal and a zero in order to work through this. Bring the decimal straight up. We can extend this division bar here. And we can think of this as 50 divided by 12. So how many whole groups of 12 in 50? Well, four. That gets us to 48. Now make sure that four is above the zero. Four times 12, 48. Subtract, 50 minus 48 is two. So we need to continue on. Let's use another zero that we can bring down. And now we have 20. So 20 divided by 12. How many whole groups of 12 in 20? Well, one. That gets us to 12. So one times 12 is 12. Subtract, 20 minus 12 is eight. Let's use another zero that we can bring down. And now we have 80. So 80 divided by 12. How many whole groups of 12 in 80? Well, six. That gets us to 72. So six here, six times 12, 72. Subtract, 80 minus 72 is eight. Let's use another zero and keep going here. So we have 80 again. How many whole groups of 12 in 80? Well, six. Six times 12, 72. Subtract, we get eight. Now I'm going to stop there because that pattern is going to continue on forever. So we end up with a repeating decimal here. We get 0.41 and then those sixes repeat. They will never end. So again, a repeating decimal here. Now we have different options as far as how we want to write out this decimal. The first option, 5 12th equals 0.416. And then we put a bar above the six. So we can put a bar above the repeating digit or digits if we have multiple digits that repeat. The bar is a way for us to write out repeating decimals. And in this example, the bar above the six tells us that the six repeats or we can round and we can round to whatever place we would like. But for this example, let's round to the 10th place and the 100th place. Let's start with the 10th place. So 5 12th is approximately, and I'm using the approximately symbol here since we are rounding, it's not exact. Now, as far as rounding, we have a four in the 10th place with a one to the right in the 100th. So this rounds to 4 10th. 5 12th is approximately 4 10th. How about rounding to the 100th place? Well, 5 12th is approximately, we have a one in the 100th, and then a six in the 1000th. So we round up here. 5 12th is approximately 42 100th. So there are some options as far as working with repeating decimals. Let's move on to numbers three and four. Here are numbers three and four. Let's jump into number three where we have nine over 16, 9 16ths. So we need to divide the numerator by the denominator. So plug in nine, the numerator, divided by 16, the denominator. This gives us 0.5625. So 5,625 10,000ths. So let's write this up here. 9 16ths equals 0.5625. Again, 5,625 10,000ths. Now, another possibility here is to round this to make it shorter. So if we get long decimals or even repeating decimals, we can round. So for example, number one, we can round to the 10ths place, 100ths place, whatever place we want to. Let's do 10ths and 100ths here. So 9 16ths is approximately, and I'm using the approximately symbol here since we are rounding, it's not exact. Let's start with the 10ths place. We have a five in the 10ths with a six in the 100ths. So we round up. 9 16ths is approximately 6 10ths. Now let's round to the 100ths. So 9 16ths is approximately, well, we have a six in the 100ths with a two in the 1,000ths. So this rounds to 56 100ths. 9 16ths is approximately 56 100ths. So some different options there as far as how we can write this out. Let's move on to number four, where we have 30 over 35, 30 35ths. So we need to divide the numerator by the denominator. So plug in 30 divided by 35. That gives us 0.857142. Those six digits repeat and go on forever in that pattern. Now it can be very hard to tell if a decimal repeats if we have multiple repeating digits and the calculator cuts the decimal off before we can tell if it repeats. This is a good example of this because depending on your calculator, you may not be able to tell if this decimal repeats based on the number of digits shown on your calculator. Now, like I mentioned earlier, what we can do if we have a long decimal or a repeating decimal, we can round. But before we round here, let's write this out as a repeating decimal. 30 over 35, 30 35ths equals 0.857142. And we can put a bar above those digits to show that they repeat. Now, our other option is to round. So let's do that. And we can round to whatever place we would like, but let's do the 10ths and 100ths place again, starting with the 10ths place. So we have 30 35ths, is approximately, well, we have an eight in the 10ths with a five to the right in the 100ths. So this rounds up to nine 10ths. So 30 35ths is approximately nine 10ths. Now let's round to the 100ths. So 30 35ths is approximately, and then we have a five in the 100ths with a seven to the right in the 1000ths. So this rounds up as well. 30 35ths is approximately 86 100ths. So there you have it. There's how to convert a fraction to a decimal. Divide the numerator by the denominator. And then if we get a repeating decimal or a long decimal, rounding is always an option. I hope that helped. Thanks so much for watching. Until next time, peace.