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CCSS.Math:

we have the million we have the number seven million three hundred forty-six thousand five hundred and twenty-one and 30 mm and what I want to think about is if I look at the same digit in two different places in particular I'm going to look at the digit 3 here and the digit 3 here how much more value does this left 3 represent than this right 3 in order to think about that we have to think about place value so let's write down all the place values so this right over here this is the ones place and we could move to the right and as we move to the right and place values each place represents one tenth of the place before it or you could divide by ten as we're moving to the right so this is the ones place this is divided by ten this is the one tenths place or the tenths place divided by 10 again this is the hundredths place divided by 10 again this is the thousandths place and that s I'm just saying to be plural hundredths thousandths now if we go to the left now each place represents a factor of 10 more so this is one's multiplied by 10 this is the tens place this is the hundreds place this is the thousands thousands place this is the ten thousands place I would have to write a little bit smaller this is the hundred thousands place and then the seven is in the millions place millions millions place so what is this number what is this 3 represent what's in the hundred thousands place it literally represents three hundred thousands three hundred thousands or you could say three hundred thousand three hundred thousand three followed by five zeros now what does this three represent it's in the hundredths place it literally represents three hundredths it represents three times one over a hundred which is the same thing as three which is equal to three over let me do the three in that purple color which is the same thing as three over a hundred which is the same thing as three over hundred which is the same which is the same thing 0.03 0.03 these are all equivalent statements now let's try to answer our original question how much larger is this 3 then that 3 there well one way to think about it is how much would you have to multiply this 3 by to get to this 3 over here well one way to think about it is to look directly at place value so we got to multiply by 10 every time we multiply by 2 every time we multiply by 10 that's equivalent to thinking about shifting it to one place to the left so we would have to multiply by 10 one two three four five six seven times so multiplying by 10 seven times let me write this down so this multiplied by ten seven times should be equal to this let me rewrite this 300,000 should be equal to should be equal to 3 over 100 let me write it the same way 3 over 100 3 over 100 multiplied by 10 seven times so times 10 times 10 times 10 times 10 times 10 let's see that's five times times 10 times 10 now multiplying by some by 10 seven times is the same thing as multiplying by one followed by seven zeroes every time you multiply by 10 you're going to get another zero here so this is the same thing as 3 over 100 3 over 100 times times one followed by one two three four five six seven zeroes so this is literally 3 over 100 times 10 million so let's see if this actually is the case is this actually equal does this actually equal 300,000 300,000 well if you if you divide 10 million by 100 well you could dividing 10 million by a hundred or I guess you could say in the numerator you have 10 million in the denominator you have 100 if you just multiply it like this if you view this as 3 over 100 times 10 million over 1 well you divide the numerator by 100 you're going to get rid of two of these zeros divide the denominator by 100 you're going to get rid of this 100 here and so you're going to be left with 3 times and we've got to be careful with the commas here because since I removed two zeros the commas are going to be different it's going to be three times we put our commas in the right place so just like that so this simplifies this simplified to three times 100,000 which is indeed 300,000 so it did work out shifting the three one two three four five six seven decimal places makes that three worth one followed by seven zeroes more or it essentially makes that three worth 10 million more so this 3 is represents 10 million times the value of this 3 let me write down the numbers so this 3 is 10 million 10 million 10 million times the value of that 3