Understanding place value
Sal discusses how a digit in one place represents ten times what it represents in the place to its right. Created by Sal Khan.
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The 4 in the number 5,634 is blank times blank than the 4 in the number 12,749. So let's think about what they're saying. So the 4 in the number 5,634, that's literally in the ones place. It literally just represents 4. Now, the 4 in the number 12,749, that 4 is in the tens place. It represents 40. So this 4, it's a 10 times smaller value than this 4. Or this 4, I should say. This 4 right over here represents 4, while this represents 40. So it is 10 times smaller than the 4 in 12,749. 4 by itself is 10 times smaller than 40. Make sure I got the right answer. Let's do another one. In the number 3,779,264, how many times less is the value of the second 7 than the value of the first 7? How many times less is the value of the second 7 than the value of the first 7? So the second 7 right over here, that's in the ten thousands place. It literally represents 70,000, 7 ten thousands, or 70,000, while this represents 700 thousands, or 700,000. So the second 7 is 1/10 the value of the first 7. Or another way of thinking, it's 10 times less. This is 70,000, and this is 700,000. So the value of the second 7 is 10 times less than the value of the first 7. Let's do one more. This is fun. Fill in the following blanks to complete the relationships between 25,430 and 2,543. All right, so 25,430 is 10 times larger than 2,543. Literally, you take this, you multiply it by 10, you're going to get 25,430. The digits in 25,430 are one place to the blank of the digits in the number 2,543. Well, let's think about it. Here you have a 2 in the thousands place. Here you have a 2 in the ten thousands place. Here you have a 5 in the hundreds place. Here you have a 5 in the thousands place. And we could keep going. But what we see is a corresponding digit. In 25,430, they're one place to the left of the digits right over here. Now, finally, we're going to take 25,430 and divide it by 2,543. Well, we already know that the first number is 10 times larger than this number right over here. So literally, if you divide the smaller number into the larger one, you're going to get 10. This right over here is 10 times larger than this. So that was the first part of the question, and we are done.