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CCSS.Math:

let's talk about multiplying by ten a hundred and a thousand there's some cool number patterns that happen with each of these so let's start here with something like four times ten one that maybe we're comfortable with or already know four times ten would be the same as saying for tens for tens and for tens one way we could represent that is a ten plus a second ten it's a third 10 plus a fourth 10 or four tens and now let's count that 10 plus 10 is 20 plus 10 is 30 plus 10 is 40 so our solution is 40 or a four with a zero and this is the pattern that we've seen before when we multiply 4 times 10 we keep our whole number of 4 and we add a zero to the end for the times 10 so another example of that might be something like 8 times 10 well 8 times 10 is the same as 8 tens and this time let's just count them if we count eight tens it'll be 10 20 30 40 50 60 70 80 so when I counted eight tens the solution was 80 or an eight with a zero on the end so times 10 when we multiply a whole number times 10 the pattern is that we end up adding a zero to the end of our whole number so let's take now what we already know about tens and let's apply it to hundreds something like let's say 2 times 100 there's a couple ways we can think about this one way is to say that this is the same as two hundreds two hundreds which is 100 plus another hundred there's quite literally two hundreds which is a total of two hundred or two with two zeros on the end now we have two zeros on the end or another way to think about this is to two times 100 instead of saying times 100 we could say times 10 times 10 because 10 times 10 is the same as a hundred and two times ten we know is a two with a zero on the end which is 20 and 20 times 10 then will be 20 with a zero on the end because we multiplied by 10 twice we added two zeros and multiplied by 100 is just that it's exactly that it's multiplying by 10 twice so if x 10 adds 1 0 then times 100 or times 10 twice adds two zeros to our answer and we can go even further and think about thousands let's try something like 9 times 1,000 well we could think of this as 9 thousands and if we have nine thousands then we have 1,000 2,000 3,000 4,000 5,000 that was 5 6,000 7,000 8,000 9,000 so when I counted a thousand nine times our solution was nine thousand or looking at the numbers a nine our original whole number with three zeros after it so nine times a thousand is nine thousand or nine with three zeros and we can go back to what we did before of thinking about this in terms of tens we've worked out why multiplying by 10 adds a zero so let's think about 1,000 in terms of tens 1000 is equal to 10 times 10 times 10 10 times ten is a hundred and 110 is a thousand so instead of 1000 we can write 10 times 10 times 10 these are equivalent and so when we multiply a number times 10 we add a zero but here we're multiplying by three tens so we add three zeros so let's look at that all as one pattern let's say something let's take seven and number seven and let's multiply it by ten by a hundred and by a thousand and see what happens seven times ten is going to be seven with one zero because we have 110 seven times a hundred will be seven with two zeros because again 100 is the same as ten times ten so this is seven times ten twice so we have two zeros and seven times a thousand will be seven thousand or seven with three zeros because a thousand is equal to 10 times 10 times 10 or three tens so we add one two three zeros and so we can see the pattern here when we multiply by ten which has one zero we add one zero to the end of our whole number when we multiply a whole number times a hundred which has two zeros we add two zeros for hundreds and for thousands when we multiply by one thousand we'll add three zeros to the end of a whole number