Video: The Expanded Form of Numbers

Which of the following expressions is equivalent to 18090? [A] 18 + 90 [B] 10000 + 8000 + 900 [C] 180 + 90 [D] 10000 + 8000 + 90 [E] 1000 + 800 + 90

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Video Transcript

Which of the following expressions is equal to 18090? 18 plus 90, 10000 plus 8000 plus 900, 180 plus 90, 10000 plus 8000 plus 90, or 1000 plus 800 plus 90.

The five-digit number that’s in our question contains the digits one, eight, zero, nine, and then another zero on the end. Now, if we look carefully at all of the additions of our possible answers, we can see that they all contain the same digits, a one, an eight, a nine, and some zeros. So this question must be getting us to think about what the digits in our number are worth. In particular, those that aren’t zero. So that’s the one, the eight, and the nine.

Now, one thing we know about adding numbers, we don’t just mash them together and write them next door to each other. So, firstly, we know that 18 plus 90 doesn’t suddenly become 18090 by writing a zero in the middle of them. In the same way, the third answer is not correct either. We don’t just write 180 and then 90 on the end to get an answer of 18090. Numbers don’t work like that. Instead, let’s think about what the digits in our number are worth and then look for an addition that shows this. Let’s use a place value grid to help us.

Let’s write our five digits in the correct places then. 18090, so what’s the one digit in our number worth? It’s in the ten thousands column. And so, it’s equal to one lot of 10000, which is 10000. The digit eight is in the thousands place. And so, this is worth eight lots of 1000, which is the same as 8000. We don’t need to worry about the next digit along because it’s a zero. Its worth is zero. So our next significant digit is nine. This is in the tens place. And it has a value of nine tens, which is equal to 90. And, of course, the final zero is worth zero. So we don’t need to worry about it.

So our number 18090 is made up of 10000, 8000, and 90. And if we look carefully, we can see the addition that shows this. Some of the other additions might look very similar. But they don’t give the digits the correct value. A good example of this is the second one on our list here. The one is worth 10000. The eight is worth 8000. But can you see that the nine in this addition is worth 900 not 90? So it was very useful that we drew that place value grid to see that the nine was worth nine tens and not nine hundreds. The expression that’s equal to 18090 is 10000 plus 8000 plus 90.

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