Video: Using Place Value to Write Numbers in Expanded Form

Which of the following equals 75 hundreds + 6 tens + 6 units? [A] 7000 + 60 + 6 [B] 700 + 110 + 6 [C] 7000 + 500 + 60 + 6 [D] 5000 + 700 + 60 + 6

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Video Transcript

Which of the following equals 75 hundreds plus six tens plus six units? 7000 plus 60 plus six. 700 plus 110 plus six. 7000 plus 500 plus 60 plus six. Or 5000 plus 700 plus 60 plus six.

What do we notice about all our possible answers? They’re all additions. It’s almost as if the answer’s been split up. Well, that’s exactly what they do show, a number that’s being expanded. And we call this expanded form. This is where a number can be split up according to its digits and written as an addition. So 123 can be written as 100 plus 20 plus three. And this helps us to understand the place value of each digit. But which possible answer equals 75 hundreds plus six tens plus six units.

Let’s work backwards with the smallest value digit. And we’ll try to narrow it down and to work out which of the four answers is correct. The smallest value part of our number is six units. Units are another way of saying ones. And so the value we’re looking for has to have six ones in it. The number that it represents has a six in the ones place. Which of our possible answers show six units as part of it? They all do. So we can’t narrow the answer down yet.

Let’s consider the number of tens. We’re told to look for the number that equals 75 hundreds plus six tens plus six units. We know that a number with six tens has a six in the tens place. And we also know that those six tens are worth 60. 10, 20, 30, 40, 50, 60. So we noticed all our additions had six units. But which have six tens? The first answer does. The second answer doesn’t. So let’s put a line through the second answer. And then the third and the fourth answers both have 60, which is the same as six tens.

Next, we need to think about the number of hundreds in our answer. We’re told that it needs to contain 75 hundreds. But how can we have a value of 75 hundreds when we can only write one digit in the hundreds place. Is 75 hundreds equal to 7000? 7000 plus 500 or 5000 plus 700. 75 hundreds are worth 7000 plus five hundreds. And so the answer is 7000 plus 500 plus 60 plus six. This has a value of 7566. This is just a four-digit number. And we can’t see the value of each digit. This is why expanded form is a really good way of showing what each digit is worth. You may have noticed the arrow cards that we’ve been using to build up the numbers as we’ve been thinking about it. If we split up our arrow cards, it’ll show the answer.

So which of the following equals 75 hundreds plus six tens plus six units? 7000 plus 500 plus 60 plus six.

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