Converting a Decimal to a Fraction | Math with Mr. J

[Music] Welcome to Math with Mr. J. In this video, I'm going to cover how to convert decimals to fractions. We'll first go through some example problems together and then I'll give you some practice problems that you can try on your own. Let's jump into our examples starting with number one where we have 0.9 9/10. Now when we convert a decimal to a fraction, we need to take a look at the place the decimal ends. So does it end in the tths, hundreds, thousandths, 10,000s or whatever the case may be, we use that place to determine the denominator of the fraction. And then whatever number we have on the right side of the decimal, so the decimal digit or digits will be the numerator. For example, number one, we have a 9. That's going to be our numerator. Now, that decimal ends in the 10th's place. So, our denominator is going to be 10. So, 9 over 10. 9/10. Now, once we have the fraction, we can look to simplify if possible. 9/10 is in simplest form. The only common factor between 9 and 10 is 1. So again this fraction is in simplest form. Now if we look at the decimal we can read that as 9/10. And then looking at the fraction we can read that as 9/10. These are equal. One is just a decimal the other a fraction. Let's move on to number two where we have 0.09. So 9 hundredths. This looks similar to number one. We have a nine on the right side of the decimal, but that decimal ends in the hundredth's place. So our denominator is going to be 100. So 9 over 100. 9 hundreds. The only common factor between 9 and 100 is 1. So this is in simplest form. Moving on to number three, we have 0.2. 2/10. Two is going to be our numerator and this decimal ends in the tenth's place. So 10 is going to be our denominator. So 2 over 10 210. Now this fraction is correct. 2/10th is correct. But we can simplify here. We have a greatest common factor of two that we can divide the numerator and denominator by. 2 / two is 1 and then 10 / two is five. So we get 1 over 5 1/5. The only common factor between 1 and 5 is one. So this is in simplest form now. So 2/10th as a decimal equals 2 / 10. 2/10th as a fraction. And we were able to simplify that fraction to 15. Let's move on to number four where we have 0.75 75 hundreds. Here we have 75 to the right of the decimal and this decimal ends in the hundredth's place. So 75 is our numerator and then 100 is our denominator. 75 over 100 75 hundreds and this is correct but we can simplify here. We have a greatest common factor of 25 that we can divide the numerator and denominator by 75 / 25 gives us 3 and then 100 / 25 gives us 4. So we get 3 over 4 34s. The only common factor between 3 and 4 is 1. So this is now in simplest form. Moving on to number five, we have 0.014 14,000. We have 14 to the right of the decimal and this ends in the thousandth's place. So 14 is our numerator and then 1,000 is our denominator. So 14 over 1,00 14,000. And this is correct. But we can simplify. We have a greatest common factor of two that we can divide the numerator and denominator by. 14 / 2 is 7. 1,00 / 2 is 500. So 7 over 500 here is 7 500s. The only common factor between 7 and 500 is 1. So this is in simplest form. And then lastly, let's move on to number six where we have 3.36 3 and 36 hundreds. So for this one, we have a whole number, which don't let that throw us off. All we need to do is focus on the decimal and do the same thing we did for all of the other examples. So we can start by writing our whole number three and then we worry about the decimal. So we have 36 to the right of the decimal and it ends in the hundreds. So 36 is our numerator and then 100 is our denominator. So we get 3 and 36 over 100. 3 and 36 hundredths. So whenever we have a whole number like that, we just rewrite the whole number and then we can focus on the decimal being converted to a fraction. Now 36 hundreds can be simplified. We have a greatest common factor of four that we can divide the numerator and denominator by. So we rewrite our whole number and then focus on that fraction. 36 / 4 is 9. And then 100 divided 4 is 25. So we get three and then 9 over 25. 3 and 9 25ths. The only common factor between 9 and 25 is 1. So this is in simplest form. So those were our example problems. Let's move on to some practice problems that you can try on your own. So have paper and a pencil ready. So, here are your practice problems. I'll give you four minutes and then we will go over the answers. Feel free to pause if you need more time or jump ahead to the answers whenever you are ready. Now, keep in mind most of these fractions can be simplified. I'll show both non-simplified fractions and simplified fractions when we get to the answers. So, it's up to you as to whether you want to simplify or not. Go ahead and start. [Music] [Music] [Music] [Music] [Music] [Music] Hey, hey, hey. [Music] [Music] Heat. Heat. [Music] [Music] Heat. Heat. [Music] Heat. Heat. [Music] Dig down. [Music] Okay, so that was 4 minutes. Let's go over the answers. So here are our answers. For number one, our fraction should be 3 over 100. 30 hundredths. For number two, we should have 55 over 100 55 hundreds, which can be simplified to 11 over 20 11 20ths. Moving on to number three, our fraction here 8 over 10, 8/10, which can be simplified to 4 over 5, 4 fths. For number four, our fraction here 6 over 1,00 6,000 which can be simplified to 3 over 500 3 500s. And then for number five, our fraction here, 3 over 10, 3/10th. And then lastly, number six, we have a mixed number here. We have a whole number and a fractional part. Our whole number is seven. And then for our fractional part, we should have 48 over 100, 48 hundredths, which that fractional part can be simplified to 12 over 25, 125ths. So there you have it. There's how to convert decimals to fractions. I hope that helped. Thanks so much for watching. Until next time, peace.