What is the closest number to 7000 that can be formed from four different digits using zero, five, seven, and four.
We’ve been given the digits zero, five, seven, and four. We need to use these digits to make the closest number to 7000 And we’re told that we need to use four different digits, which means that we just need to rearrange these digits to form our number. So what sort of number we looking for? Let’s write 7000 on a number line. The multiple of 1000 before 7000 is 6000. And a multiple of 1000 that comes after 7000 is 8000. If we’re looking for a number that’s close to 7000 and is less than 7000, then we’re looking for a number that’s going to be 6000 and something.
If we look at our digits, we don’t have a six, so we can’t make any of the numbers in this area. And if we wanted to make a number that was close to 7000 but was greater than 7000 then we’re thinking of a number that is going to be 7000 and something. Well, we can see that we do have the digit seven. If we begin with a five or a four, our number is going to be a lot further away from 7000. But if we begin with the digits seven, we’re going to find the closest number to 7000. So let’s start by taking our card with the seven digit and let’s put it in the thousands place. Our number is going to be 7000 and something.
Now, let’s alter our number line to help us focus on the part where our number belongs. We’ll put 7000 at one end and 8000 at the other. We know that the halfway point will be 7500. To make our numbers close to 7000 as possible, we need to choose the smallest digit. If we choose the five, our number is going to be 7500 and something. If we choose the four, it will be 7400 and something. But look how close to 7000 our number will be if we choose the smallest possible digit, the zero. Our answer will just be 7000 and something.
So let’s take the zero digit and put it in the hundreds place of our number. We can see that our number now has seven thousands and zero hundreds. We only have the digits, five and four, left. So we can see that we’re either going to make one of two numbers, 7045 or 7054. Let’s think about which did it to choose and we’ll alter our number line one more time. This time, we’ll just show the part between 7000 and 7100. These are all the numbers that have seven thousands and zero hundreds. And in the middle is 7050. So we know 7054 will probably be about here. But 7045 will be less than 7050. That will be about here.
Once again to keep our numbers close to 7000 as possible, we need to use the smallest digit. So we’ll take the four digit and we’ll put it in the tens place. And then we’ll take the five digit. And we’ll put it in the only place we have remaining in the ones place. We were asked to make the closest number to 7000 as we could. And we’ve made a number that’s only 45 away from 7000. We rearranged the digits zero, five, seven, and four. And the closest number to 7000 that we could make was 7045.