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CCSS.Math:

multiplying by 10 creates a really neat pattern with numbers so let's try a few out and see if we can discover the pattern let's try to figure it out we'll start with one that maybe we already know let's start something like 2 times 10 and maybe we know the solution but let's think about more than just the solution let's think about what it really means to multiply 2 times 10 2 times 10 means we have two tens or we have a 10 plus another 10 which is equal 10 plus another 10 is equal to 20 and again maybe we didn't need this middle part maybe we already knew 2 times 10 was 20 but it'll be helpful to think about what 2 times 10 means because it will help us when we get to much trickier ones let's try one that's maybe just a little bit trickier let's try 5 times 10 5 times 10 is going to be 5 tens or 110 plus another 10 plus a third 10 plus 1/4 10 plus 1/5 10 so we have 5 tens we have 1 2 3 4 5 tens and we can solve that we can add those together 10 20 30 40 50 so our solution here is 55 tens is 50 or 5 times 10 is 50 let's go to one more maybe one that we don't know the answer to off the top of our head let's try something like 13 times 10 maybe we don't know the answer to 13 times 10 but we do know that 13 times 10 is 13 tens and we can count 13 tens we'd have a 10 plus another 10 plus another there's 3 4 5 6 tens 7 8 9 10 we're almost there Oh living tens twelve tens and finally a thirteenth 10 let's count to make sure one two three four five six seven eight nine ten eleven twelve thirteen great so we have thirteen ten so let's count those let's see how much that is we have 10 20 30 40 50 60 70 80 90 100 110 120 130 so our solution is 130 I think we can pause here and look at the ones we've done so far and see if we can figure out this pattern 2 times 10 is 20 5 times 10 50 13 times 10 130 in every case we took the number that we started with and we kept that that was part of our answer and then we added one new thing which was a zero at the end any time we multiply a whole number by 10 we're going to keep the original number and simply add a zero to the end so let's try some without all this middle stuff what if we had something like a little bit tougher maybe like 49 times 10 well 49 times 10 you may guess it is going to be a 49 with what at the end zero or 490 because this would be 49 tens and if we counted 49 tens we would get to 490 let's go even tougher than that what if we had something like 723 times 10 well our solution and maybe you've guessed it is going to be 723 with a zero on the end or 7230 is the way we would actually read that answer but looking at it it quite simply is the number 723 with a zero on the end let's take this one step further and let's think about it in terms of place value let's think what multiplying by tended to these numbers in terms of their place values so here we have a place value chart and let's start back with one of the simpler ones we did like two two is two ones but when we multiply that 2 times 10 the two moved up a place value and then we had to fill in this empty place value with a 0 so 2 times 10 was 20 and what happened in terms of place value was the two moved up one place value it went from ones to tens and move to the left one place value let's look at another one maybe one of the tougher ones something like 723 when we multiplied 723 times 10 we multiply this one times 10 the 7 moved one place value to the left to the thousands the 2 moved up to the hundreds and the 3 moved up to the tens and then again we simply added a 0 in the empty place value in the end so multiplying by 10 one way to describe the pattern is that it adds a zero to the end of a whole number but another way to describe the pattern is that it moves every place value every number 1 place value to the left so if we tried 1 looking at it this way let's say we tried something like a 20 let's do 27 if we multiply 27 times 10 well the 2 is going to move one place value over so it will now be in the hundreds and the 7 is going to move over a place value so it will be in the tens and then we'll have to fill in that empty place value with the zero so we can say that 27 times 10 is equal to 270 so whether we think about it as adding a zero to the end or moving a place value to the left multiplying by 10 creates a really neat pattern that we can use to help us to solve these problems