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# Multiplying and dividing decimals by 10, 100, 1000

CCSS.Math:

## Video transcript

in this video we're gonna get a little bit of practice multiplying and dividing decimals by ten hundred and a thousand so let's just start with a little bit of a warm-up if I were to say what is two point zero five times ten pause this video and see if you can figure that out well in previous videos result we've already said that when you multiply by ten you shift each of the digits one place to the left and so this is going to be equal to instead of two ones we're not going to have two tens so two in the tens place and then instead of zero tenths we're now going to have zero ones and instead of five hundredths we're now going to have five tenths so this is equal to twenty point five now what if we were to go the other way around what if we were to say two point zero five divided by 10 pause the video and see if you can figure that out well here all of our digits are going to shift one place to the right because we're dividing by ten we could also view that as multiplying by one tenth and so our two ones are going to become two tenths so this is going to be zero point so we're gonna have two tenths now our zero tenths are going to be zero hundredths and then our five hundredths are going to be five thousandths and we've covered that in other videos but now let's do this with say a hundred or a thousand so if I were to ask you what is 57 divided by 1,000 pause this video and see if you can work that out all right now let's do this together so when you divide by a thousand that's the same thing as dividing by 10 three times or it's the same thing as multiplying by 1/10 three times or you could just say hey that means I'm going to shift each of these digits three places to the right and so let me create some places here so there's tens ones tens hundreds thousands and so five was in the tens place it's five tens so it was here but we're going to shift three places to the right one two three so our five will go there so what was five tens is now five hundredths and then our seven is similarly going to it was in the ones place but we're going to shift three places to the right one two three and there you have it what was just 57 is now fifty-seven thousandths and to make that very clear I'll put a zero in the tenths place and a zero in the one place in the ones place and that makes sense so it's another example let's say someone walks up to you on the street and says I started with one 0.03 two and I multiplied it by something and I was able to get one hundred and three point - what did they multiply by to get one hundred and three point to pause this video and try to work it out well to understand this we just have to think well how much did the each digit get shifted by so what was in the ones place got shifted not just to the tens place but it got shifted to the hundreds place so it got shifted two places to the left the zero similarly got shifted two places to the left from the tenths to the tens and if you look at it every digit got shifted two places to the left and so we must have multiplied by 10 twice so you could say times 10 times 10 or you could just rewrite this as times 100 let's just do one more example for kicks let's say that someone were to say what is 0.01 5 times 100 pause this video and see if you can figure that out all right well like we've done before we're just going to shift every digit two places to the left so the one which is in the hundredths place is going to end up in one's place and then the five which is in the thousands place is going to end up in the tenths place so this is going to be equal to one point five and we're done