Ali puts these five numbers in their correct places on a number line: 511, 499, 502, 555, and 455. Write the number closest to 500 and write the number furthest from 500.
In this problem, we’re given five three-digit numbers. And both parts of the problem ask us to compare those numbers to the number 500. First, we’re asked to write the number that’s closest to 500. And then in the second part of the problem, we’re asked to write the number that’s furthest away from 500.
At the moment, the numbers are not in the right order. You can find the answer without ordering them correctly. But being as though Ali puts the numbers in the correct places on a number line, let’s do this because it will certainly help us if we can see them all in the correct order.
Here’s our blank number line. The numbers either have four hundreds or five hundreds. So the smallest number is going to be a number that starts with four hundreds. Well, there are two of those. So let’s compare the tens. Five tens is smaller than nine tens. So the first number on our number line is 455, and the second number is 499. Let’s put a tick by those numbers to show that we’ve dealt with them already.
If we compare the hundreds digits of the remaining three numbers, they all have five hundreds. So we now need to compare the tens. Zero tens is the smallest. So our next number is 502. One ten is the next smallest. So the next number in order is 511. This means the largest number out of the five is 555.
Now that we’ve written the numbers in order, it will help us compare them to the number 500. So the first part of our problem is to write the number closest to 500. Where is 500 on our number line?
Well, it’s in between two numbers: 499 and 502. One of these two numbers is the closest to 500. Which is closest? To get from 499 to 500, we add one. The number is one away from 500. To get from 500 to 502, we add two. The number is two away from 500. And so the number closest to 500 is 499.
The second part of our problem asks us to write the number furthest from 500. As before, we have two possible answers. To the left of 500 on our number line, which are all the numbers that are lower than 500, the furthest away is 455. And to the right of 500 — that’s all the numbers that are greater than 500 — the furthest away is 555. Which of these two numbers is furthest from 500?
455 is 45 away from 500, because if we add 45 to it, we make the next hundred. And 555 is 55 away from 500. So although we don’t have to draw a number line to help us with this problem, it does help, particularly because the number 502 does look very close to 500.
So it’s an easy mistake to make to put that as the answer to the first part. However, we worked out that the closest number to 500 is 499 and the number furthest from 500 is 555.