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## Arithmetic (all content)

### Course: Arithmetic (all content)>Unit 1

Lesson 9: Ways to write whole numbers (expanded form and written form)

# Writing a number in standard form

This video demonstrates converting large numbers from expanded and written form to standard form. Using the example "six hundred forty-five million five hundred eighty-four thousand four hundred sixty-two," it explains the process and arrives at 645,584,462, emphasizing place value understanding. Created by Sal Khan and Monterey Institute for Technology and Education.

## Video transcript

Write six hundred forty-five million five hundred eighty-four thousand four hundred sixty-two in standard form. So let's tackle this piece by piece. So the first part we have six hundred and forty-five million. So let's think about that. So we have six hundred and forty-five. But it's not just six hundred forty-five. We have six hundred forty-five millions. So we could view that as 645 times 1,000,000. One million is one followed by six zeroes. So this piece right here is this right over here. That is six hundred and forty-five million. And what is that when we write it out? If we were to multiply this out, this is equal to-- it would be 645 times this 1 with six zeroes behind it. So this would be equal to 600-- I'll write it like this. This is equal to 645, and then we have our six zeroes. One, two, three, one, two, three. That's just this part of the number. And I'm going to do it kind of slow and do all of the different parts of the problem, but once you get some practice, you'll find that these are a bit second nature, and you won't have to go through all of these steps. You'll just be able to write the number. Now, let's move on to the next part. We have five hundred and eighty-four. Let me write that down. Well, I'll write it like this. 584 thousand. So let me write the thousand. So 584 thousand. So it's 584 times 1,000. And what's that going to look like? So that's this whole part right here. So 584 times 1,000 is equal to what? Well, it's going to be 584 with three zeroes behind it, or you could view it as 584 times the 1, and then you're going to have three zeroes in the final answer. So it's going to be 584,000. We have our three zeroes at the end. 584, three zeroes. So that's that part. And then finally, we have four hundred sixty-two, and that's just 462, straight up. You could view it as 462 ones. So then you just have 462, which obviously equals just 462. Now our number is all of these combined. It is 645,000,000 and 584,000 and 462. So one way to think about it is that you could add these three numbers. So if we were to add them, we get 645,584,462. Now, I said it'll become a little bit of second nature to you in a little bit, and the way to think about that, the easiest way to think about that, is millions will have six zeroes behind them, thousands will have three zeroes behind them, and just regular numbers have no zeroes behind them. So what you can do when you kind of want to learn it second nature, you'll just look at the six hundred and forty-five million, so you'll write 645, and you'll kind of keep in the back of your mind that you're going to have to have six more digits to the right of this. And then you say five hundred and eighty-four thousand, so then you have your five hundred and eighty-four thousand, so then you write that down, 584,000, keeping in mind that you're going to need three digits to the right of that. And so if they didn't tell us 462, we would just put three zeroes here, and that would also fulfill the six zeroes we need behind 645,000,000. But then they tell us 462, so we just write that right here. 462.