Question Video: Converting a Number from Expanded Form to Standard Form Mathematics

What is 10,000 + 2,000 + 50 + 5 in standard form?


Video Transcript

What is 10,000 plus 2,000 plus 50 plus five in standard form?

In this question, we’re given what looks like an addition, but this is more than an addition. This is a number that’s been written for us in what we call expanded form. Expanded form is a way of writing a number as an addition by showing the value of each of its digits. So we can see with the number that’s being talked about here we’ve got a digit that’s worth 10,000. There’s going to be another digit that’s worth 2,000, one that’s worth 50, and then a digit that’s worth five.

Now, we’re asked to write this number in standard form, in other words, the way that we usually write a number using digits. Because there are four parts to our addition, do you think it’s gonna be a four-digit number? Well, if we look closely, we can see that there’s one type of digit missing. Did you spot it?

Let’s use a place value grid to help us see which one. The first number in this addition is 10,000. So we need to use a digit that represents this value. To show 10,000, we need to write the digit one in the ten thousands place. One lot of 10,000 is 10,000. The next number in our addition is 2,000. So which digit do you think our number has in it and where should we write it?

Well, for a digit to be worth 2,000, it needs to be the digit two and it needs to appear in the thousands place. Our next number is 50. How would we represent 50 in our place value grid? 50 is the same as five 10s. So we need to write the digit five in the tens place. Can you see what’s happened here? We haven’t been given a number of hundreds. We still need to show that there’s an empty hundreds place though, and so we can use zero as a placeholder. And that’s why even though we’ve been given four parts to our addition, it’s actually a five-digit number. We just don’t have any hundreds. Finally then, we need to add five. And to show five in our number, we just write five in the ones place.

We recognized that the addition in the question was a number written in expanded form. To write this number in standard form, we thought carefully about how to create these values by writing digits in the right places. The number is 12,055. And we write this in standard form by writing the digits one-two-a comma-zero-five-five.

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