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# Dividing a whole number by a decimal

Dividing a whole number by a decimal can be simplified by multiplying both numbers by 10, shifting the decimal point to the right. For example, dividing 518 by 0.7 becomes 5,180 divided by 7. Using long division, the result is 740, making the process easier and more manageable. Created by Sal Khan.

## Want to join the conversation?

• in do you have to put the zeros? I'm just making sure.
• Also think of it this way: 540.0 =540.0000000000
• what do i do when i can not concentrate when my friends are talking?
• tell them, ''be quiet, please'' :]
• Why is there a green dot in the center in the whole video?
• is it possible to make 1000000000000000 in a fraction
• I think so it would be like 1000000000000000/1
• at do you need the zeros
• Since adding as many zeroes as wanted behind the decimal point (for example 7 = 7.0000000) never changes the number, one can do it. You don't need the zeroes, but the problem is a lot easier if you add them.
• Is there an easier way of doing this math, or any helpful tips?
• Here are tricks for dividing by some common decimals.

1. Dividing by 0.5 is the same as multiplying by 2.

2. Dividing by 0.25 is the same as multiplying by 4.

3. Dividing by 0.2 is the same as multiplying by 5.

4. Dividing by 0.1 is the same as multiplying by 10.

5. Dividing by 0.05 is the same as multiplying by 20.

6. Dividing by 0.02 is the same as multiplying by 50.

7. Dividing by 0.01 is the same as multiplying by 100.

Have a blessed, wonderful day!
• I have a math problem it is 40 divided by 1.25. This video didn't really help me with this problem but if any of you guys know how to help me please leave a comment. Thanks
• Just move the decimal 2 places to the right so it becomes 4000 divided by 125.
• why do we put the decimal point there?
• Do we have to move the decimal how many times we moved the decimal at first? On , this question makes it hard to understand what you did.
• Why would you multiply by 10? Why, not 100?
• As Sal stated, the best way to do it is to turn .7 into a whole number, and multiplying by 10 is the simplest whole number which also makes the problem the simplest. If you have two decimals such as .45, it would be better to multiply by 100 to make the simplest whole number.

## Video transcript

Let's divide 518 by-- so we're going to divide it by 0.7. So we're dividing this whole number by a decimal. So we could also write this as 518 divided-- let me write a little bit bigger than that, since we have to do some work with it. 518 divided by-- I'll do the division sign in white-- divided by 0.7. So the first thing we do, since we have this decimal here, we're dividing by a decimal. So try to turn this into a whole number somehow. Well, the best way to turn this into a whole number is to multiply this by 10, which is essentially multiplying, shifting the decimal point over to the right. So this would become a 7. But we can't just do that only for what we're dividing by. We also have to do that to the 518, so that a value does not change. So we need to multiply both of these times 10. So if we move the decimal over to the right with the 0.7 to turn into a 7, we also need to move the decimal over to the right for 518. Now, you're probably saying, well, I don't see a decimal in 518. Well, there is one. You just didn't have to write it, because it's 518.00-- and we can add as many zeroes as we want. So if we move the decimal to the right, it becomes 5,180. So really what we're saying is 518 divided by 0.7 is the same thing as 5,180 divided by 7. Notice all we did by moving the decimal one place to the right, is we multiplied both of these numbers by 10, which is not going to change the actual value of the decimal. One other way of thinking about this, if you wanted to write this as a fraction, this is the same thing as 518 over 0.7. You multiply both the numerator and denominator by 10, you will get 5,180 over 7. So let's clean this up a little bit, just so we remember what we did. So we moved the decimal over to the right, one. So now this is just a 7. The decimal is there. In fact, we really don't have to write the decimal anymore. It's just a 7.0-- you could imagine 7.0, so we can just write this as a 7. And then the 518, the decimal is now out here. So this is 5,180. And let's increase the sign right over here. Now, this is just a straight-up long division problem. How many times does 7 go into 5? Well, it goes 0 times. 0 times 7-- actually, let's just cut to the chase. 7 doesn't go into 5. It does go into 51. 7 times 7 is 49. So it goes 7 times. 7 times 7 is 49. Subtract 51 minus 49 is 2. And now we can bring down this 8. 7 goes into 28 four times. 4 times 7 is 28. Subtract, you get a 0. Now we can bring down another 0. We want at least get to the decimal place. So we bring down another 0 right over here. When I say get to the decimal place, we could put the decimal place up here too, just to make sure we're keeping track of the right place values or that we can have the decimal in the right place. So notice, I'm very particular. When I'm doing 7 goes into 51, I put the 7 right above the 1 in the 51's place. When I'm saying 7 goes into 28, I'm putting the 4 right above the 8 in this one's place when we're doing the division. So now we say how many times does 7 go into 0? Well, it goes 0 times. 0 times 7 is 0. Subtract, you have no remainder. So we could keep going, and we'll just keep getting zeroes like this. But we see that this is equal to 740.