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# Multiplying and dividing by powers of 10

CCSS.Math:

## Video transcript

in another video we introduced ourselves to the idea of powers of 10 we saw that if I were to just say 10 to the first power that means that we're just really just going to take 110 if we have 10 to the second power that means that we're going to take two tens so a 10 and a 10 and we're going to multiply them and so that's going to be 100 if we take 10 to the third power that's going to be three tens multiplied together which is equal to 1,000 which is also one followed by three zero so you're already starting to see a pattern what we're going to do in this video is think about patterns when we multiply arbitrary things or divide our buri things by powers of 10 so let's start with a number let's say I will start with 2.3 and let's first just multiply it by 10 to the first power well that's the same thing is just multiplying it by 10 and we've seen already when you multiply by 10 you shift all the digits one place to the left so the two which is in the ones place will end up in the tens place and then three which is in the tenths place will end up in the ones place so this is just going to be equal to 23 and it's always good to do a little bit of a reality check if I just had two and if I were to multiply it by 10 you say okay that's about 20 so it makes sense that two point three times ten is twenty three but let's keep going now let's multiply 2.3 not by ten to the first power which is just ten but let's multiply it times ten to the second power what is that going to be pause this video and see if you can figure that out all right well ten to the second power we already know that's equal to a hundred and so when you multiply by a hundred or you multiply by 10 twice you're just going to shift every digit two places to the left so let me draw some places here so the thing that is in the ones place will go to the hundreds place and the thing that is in the tenths place will go to the tens place and so this too will now be to hundreds this 3/10 will now be three tens and we now have zero ones and then if we were to multiply by ten again so if we were to say 2.3 times 10 to the third power well then we're going to shift everything three places to the left ten to the third power this is the same thing as multiplying by 1,000 so two point three times ten to the third the two is going to be shifted three places to the left so the two is going to become 2,000 which makes sense so it's going to be 2000 the 3/10 is going to shift two places to the left so it's going to be 300 and then we now have zero tens and zero ones so the pattern that you've probably seen is if you multiply a number times 10 to some power you are just shifting the digits to the left by that power and if we divide by a power of 10 the same thing would happen but we would now be shifting our digits places to the right so for example what is 2.3 divided by divided by 10 to the first power pause this video and try to figure that out well ten to the first power is the same thing as 10 so when we divide by 10 all of our digits are just going to shift one place to the right so this 2 is going to end up in the tenths place and the 3 is going to end up in the hundredths place so this is going to give us zero point 2 3 2 is now in the tenths 3 is now in the hundredths but we could keep going what if we were to say 2 point 3 divided by 10 to the second power pause this video try to figure out what that is well in this situation we are going to shift all the digits two places to the right and so let me put my places here so that's the ones tenths hundredths thousandths and so the thing that's in the ones place is two it won't just go to the tents it'll go to the hundreds place which you don't quite see here's it's right over there so the two is going to show up here and then the three is going to shift two places to the right and so it's going to end up there and we have zero ones and we have zero tenths so you're probably already seeing the pattern here again whatever the exponent is if you're dividing by ten to that power you're going to shift that power that exponent that many times you're going to shift the digit that many places to the right