Question Video: Using Place Value to Write Numbers in Expanded Form | Nagwa Question Video: Using Place Value to Write Numbers in Expanded Form | Nagwa

Question Video: Using Place Value to Write Numbers in Expanded Form Mathematics • Third Year of Primary School

Write the following number in expanded form: 1,384 = ＿. [A] 4,000 + 800 + 30 + 1 [B] 1,000 + 300 + 80 + 4 [C] 1,000 + 300 + 40 + 8 [D] 3,000 + 100 + 80 + 4

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Video Transcript

Write the following number in expanded form: 1384 equals what. 4000 plus 800 plus 30 plus one, 1000 plus 300 plus 80 plus four, 1000 plus 300 plus 40 plus eight, or 3000 plus 100 plus 80 plus four.

We know that we can express numbers in lots of different ways. In this question, we’re given a four-digit number. And the way that it’s written in the question we’d say is it’s in digit form. We’ve just got those four digits written: one three eight four. And our question asks us to write this number in a different way. We need to write it in expanded form. We know when something expands, it gets bigger or it opens up. And if we want to write a number in expanded form, we need to take that number and open it up into its different parts. A four-digit number is made up of thousands, hundreds, tens, and ones. And so we need to split up our four-digit number into four parts.

We could sketch a part–whole model to help us here. Perhaps, we ought to call it a part, part, part, part–whole model. To begin with, let’s write our whole number, 1384. Let’s begin by looking at our first digit, one. Is it worth one, 10, 100, or 1000? Well, if we think of the four places that make up a four-digit number, we know that the first digit is the number of thousands that we have. And if there’s a one in the thousands place, this has a value of 1000.

Now, if we pause for a moment to look at our possible answers, we can see that they are four different additions. They show a number of thousands added to a number of hundreds plus a number of tens and a number of ones. Now, as we’ve seen already, the thousands digit in our number is one, and this has a value of 1000. So, can you see which answers might be correct here? It’s not the first addition because that begins with 4000. And we know it’s not the last edition either; that begins with 3000. But it could be either of the other two answers.

Let’s carry on splitting up our four-digit number. And we’re on to the second digit, three. Now, this digit is in the hundreds place, and three 100s have a value of 300. But can you see if we go back to our two possible answers, both of them show 300 being added. In fact, the only difference between them is the number of tens that are being added and the number of ones. So, let’s finish off expanding the tens and ones in our number. In the tens place, we have the digit eight. And we know that eight 10s have a value of 80. And then, finally, in the ones place we have the digit four.

And so, by looking at our part–whole model, we can say that the number 1384 can be split into 1000, 300, 80, and four. And so we can see the answer. We’ve expanded a four-digit number into its thousands, hundreds, tens, and ones. And we’ve written these as an addition, just the same as writing the number in expanded form. 1384 is the same as 1000 plus 300 plus 80 plus four.

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