Video: Using Place Value to Convert the Expanded Form of Numbers to the Standard Form

Evaluate 30000 + 7000 + 100 + 20 + 7 = _.

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Video Transcript

Evaluate 30000 plus 7000 plus 100 plus 20 plus seven equals what.

This addition is actually a five-digit number that’s been split up and written in what we call expanded form. This means that we’ve written the value of each of the five digits as a number. Five-digit numbers are made up of a number of ones, tens, hundreds, thousands, and tens of thousands. And each of these five columns or places correspond with one of the numbers in the addition. The addition is telling us what each digit in our number is worth. So if we put all these numbers back together again, it will make the single number that we’re talking about, the single five-digit number.

So to begin with, which part of our addition shows the number of ones that we have in our total? Well it’s this number here. The number seven represents seven ones. And so the digit in the ones place of our five-digit number is seven. Now, how many tens does our number have? In our addition, we can see the number 20. This shows a number of tens and no units. The number 20 represents two tens. And so we can write the digit two in the tens place of our number. The next number to the left, 100, shows us the number of hundreds in our number. 100 represents 100, zero tens and zero ones. So we can write a one in the hundreds place.

Now, how many thousands does our number? The number 7000 is made up of a seven in the thousands place, zero 100s, zero tens, and zero ones. So we need to write a seven in the thousands place. Finally, we can see the number of ten thousands in our number. 30000 is the same as three tens of thousands. We started off with a number that was written in expanded form. Each of the digits had been separated out according to what it was worth. So by adding all the numbers together, what we’re doing is putting all the separated parts back together again. Each digit still has the same value, but now they’re combined together to make the five-digit number. 30000 plus 7000 plus 100 plus 20 plus seven equals 37127.

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