Converting Between Fractions and Decimals | Fractions to Decimals | Decimals to Fractions

In this video, I'm going to cover how to convert between fractions and decimals. So fractions to decimals and decimals to fractions. Let's start with fractions to decimals. Starting with number one, where we have 1 4th. Now, when we go from fractions to decimals, we can divide the numerator, the top number, by the denominator, the bottom number. So here we need to do one divided by four. Remember, fractions are a representation of division. And if we do the division, we get the decimal form of the fraction, and they are equal. One form is just a fraction and the other a decimal. So again, one divided by four here. And I'm going to do the division by hand in this video. So let's set this up. One divided by four. So let's start with one divided by four. How many whole groups of four in one? How many fours in one? Well, we can't do that. So we need to put a decimal after one, and then a zero to the right of the decimal. And I'm going to extend that division bar there. Now, remember, zeros to the right of a decimal or to the right of decimal digits do not change the value of the number. So we're able to do this in order to work through the division problem. Now we bring the decimal straight up into the quotient, the answer. Now we can think of this as 10 divided by four. So how many whole groups of four in 10? How many fours in 10? Well, two. So let's put the two above the 10 and make sure it's above the zero. Now we multiply. Two times four is eight. Subtract. 10 minus eight is two. We don't have that clean-cut zero at the bottom here, so we can continue on. Let's use another zero that we can bring down. So now we have 20. 20 divided by four, which is five. Five times four is 20. 20 minus 20 is zero. Nothing else to bring down within our problem, and we have that clean-cut zero. We are done with the division, and we can write this over here, and I'm going to start with a zero and then a decimal to show that we are working with a decimal here. It helps us recognize we have a decimal. Helps us see the decimal. So 0.25. 1 4th equals 0.25. Let's move on to number two, where we have 5 16ths. So we need to do five divided by 16. So as far as five divided by 16, how many whole groups of 16 in five? Well, we can't do that, so we need a decimal and then a zero. Let's extend this division bar here and bring the decimal straight up into the quotient, the answer. Now we can think of this as 50 divided by 16. How many whole groups of 16 in 50? Well, three. That gets us to 48. Three times 16, 48. Subtract. 50 minus 48 is two. So we don't have that clean-cut zero quite yet, so let's use another zero that we can bring down. Now we have 20. 20 divided by 16. How many whole groups of 16 in 20? Well, one. One times 16 is 16. Subtract. 20 minus 16 is four. So let's continue on by using another zero that we can bring down. So now we have 40. 40 divided by 16. How many whole groups of 16 in 40? Two. That gets us to 32. Two times 16, 32. Subtract. 40 minus 32 is eight. So let's continue on. So another zero. Bring that down. And now we have 80. 80 divided by 16. How many whole groups of 16 in 80? Well, five. And that's going to hit 80 exactly. Five times 16 is 80. 80 minus 80 gives us that clean cut zero. We are done. So 5 16ths equals 0.3125. 3,125 10 thousandths. So let's write this over here and we will start with the zero and the decimal. Remember that zero helps us recognize we have a decimal here. So 0.3125. So 5 16ths equals 3,125 10 thousandths. Now, before we move on, I do want to mention what happens if we don't get to that clean cut zero? What happens if that decimal keeps going? In that case, we need to round. So for example, go to the 10 thousandths place and round to the thousandths. Or go to the thousandths place and round to the hundredths. Do whatever works best for you. Now let's move on to going from decimals to fractions. And all we need to do here is use place value to determine our denominator. And then we can simplify if possible. For example, number three, we have 0.7. So 7 tenths here. This decimal ends in the tenths place. That means our denominator is 10. So we write this as 7 tenths. Again, our decimal ends in the tenths place and that tells us what our denominator is, 10. And that's it. We can read the decimal as 7 tenths and the fraction as 7 tenths as well. They have the same exact value. One is just a decimal and the other a fraction. Now as far as simplifying, 7 tenths is in simplest form. The only common factor between seven and 10 is one. So we are done. Moving on to number four, this looks similar but we have 0.07. So seven hundredths here. The seven is in the hundredths place. So that's what we're going to use for the denominator. So for number four, we have seven over 100. Seven hundredths. The only common factor between seven and 100 is one. So we are in simplest form. Let's move on to number five, where we have 0.55. 55 hundredths. Now this decimal ends in the hundredths place. So that's going to be our denominator. So we have 55 over 100, 55 hundredths. Now this fraction can be simplified. We have a greatest common factor of five that we can divide the numerator and denominator by in order to simplify. 55 divided by five gives us 11 and 100 divided by five gives us 20. Now the only common factor between 11 and 20 is one. So we are in simplest form. 11 twentieths. Lastly, moving on to number seven, we have 2.42 and four tenths. Now don't let the whole number hold us up on this. All we need to do is write the whole number and then we worry about the decimal. Here we have 0.44 tenths. So the decimal ends in the tenths place. So that's going to be our denominator. So four tenths. So this is two and four tenths and this is two and four tenths. Now we can simplify the fractional part of this mixed number. We have a greatest common factor of two that we can divide the numerator and denominator by. So we have a whole number of two and then four divided by two gives us two and 10 divided by two gives us five. So this simplifies to two and two fifths. So there you have it. There's how to go from fractions to decimals and decimals to fractions. I hope that helped. Thanks so much for watching. Until next time, peace.