How 10 relates to place value
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Comparing place values
We have the number 43,249. Now, what I want you to think about is what these two 4's actually represent and how much more value is represented by this first 4, this 4 on the left, than this 4 on the right. And I encourage you to pause this video and think about that. So let's just think about what each of these digits represent. So the 9 is in the ones place. So it literally represents 9 ones. This 4 on the right, I should say, is in the tens place so it literally represents 4 tens, or 4 times 10, or 40. This 2 is in the hundreds place, so it literally represents 2 hundreds, or 200. This 3 is in the thousands place, so it represents 3 thousands. And then the 4 on the left is in the ten thousands place. So it literally represents 4 times 10,000, or 4 ten thousands, or 40,000. So let's actually compare the value that we're getting here versus here. So what's the difference between 40,000 and 40? Well, 40,000 has four zeroes while 40 only has one. So if you wanted to go from 40 to 40,000, you would have to add three more zeroes. And we already know how to do that. You could add three more zeroes by multiplying by 1,000. So 40,000 is equal to 1,000 times 40. Or we could say the 4 on the left here, this blue circled 4 represents 1,000 times the value as the yellow circled 4. Now, another way of thinking about it is every time you move place values to the left, as you see here-- this is tens, hundreds, thousands, ten thousands-- you're increasing what those place values represent by a factor of 10. So if you're going from this 4 to this 4, times 10 times 10 times 10, you multiply by 10 the place value. And you see that with the place values right over here, the place values increase by a factor of 10 each time. So if you're going from this place to this place, and you have the exact same digit there, multiplying by 10 three times is the same thing as multiplying by 1,000. So whatever this represents, multiply it by 1,000, and you're going to get what this represents.