Question Video: Using Place-Value to Complete Comparison Statements Involving 12-Digit Numbers Mathematics

Which of the following numbers could complete the expression 587,452,159,632 > _ > 587,452,150,566? [A] 588,452,150,566 [B] 587,452,157,869 [C] 587,451,150,566 [D] 587,552,150,560


Video Transcript

Which of the following numbers could complete the expression 587,452,159,632 is greater than what which is greater than 587,452,150,566. And then, we’re given four possible answers. And they are 588,452,150,566; 587,452,157,869; 587,451,150,566. Or lastly, 587,552,150,560.

Reading 12-digit numbers like this can be tricky, as can comparing them or ordering them. In this question, we need the skill of being able to read these numbers, but also to compare them. We’re given two of these 12-digit numbers as part of an expression. The expression shows us that the first number is greater than a missing number that we need to complete, but that this missing number is greater than our third number. If we say this another way, the numbers are in order from greatest to least. And we can use this to help us find the number that goes in the middle of these two numbers.

To help us read our numbers and also compare them, we can draw a place value grid. We can tell by looking at the symbols that the greatest of our numbers is the first one in the expression. We can read this as 587,452,159,632. The number that’s worth the least is the last number in our expression, which is 587,452,150,566. And we’re looking for a number that’s less than the first number but greater than the second. In other words, it goes in between. Now, what can we notice about the two numbers that are at either end of our list?

Well, they both begin with the same eight digits. They both contain 587 billion 452 million 150 something thousand. Because it’s only when we get to our thousands column that the digits in our numbers are different. So the first thing we can say about the number we’re looking for is that it must contain 587 billions 452 millions 150 thousands. The second thing that we can say about our missing number is that we might expect the digit in the thousands place to be between nine and zero. In other words, it might have a value of eight all the way down to one. This digit doesn’t have to have this value because we could compare the other columns. But let’s see if we can find the number that does.

First of all, which of our numbers contain 587 billions. We can see that one of our numbers doesn’t and the other three do. So we can cross off the one that doesn’t. 588 billions is too large. Now, which of the remaining numbers contain 452 millions? Well, we can see that only one of them does. The other numbers contain 451 millions, which is too small, and 552 millions, which is too large. It’s looking like we might know what our missing number is. We have two more things to check. Does the number contain 150 something thousand? Yes, it does. And also, does it have a digit in the thousands column that is between nine and zero? Yes, it does. It has a seven in the thousands place.

So we could complete the rest of our number in the place value grid and see that it fits between the two numbers that we’ve been given. The correct number to complete the expression that we were given is 587,452,157,869.

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