True or false? Five ones and seven hundreds is greater than 750.
The two numbers in the sentence that we’ve been given are represented in different ways. The first number is written in words, five ones and seven hundreds. But interestingly, it’s not written as a number. It’s written in such a way that we know the place value of the different digits in the number, five ones and seven hundreds. Our second number is perhaps a little easier to understand. It’s written in digits, 750.
Now, our sentence tells us that five ones and seven hundreds is greater than 750. And we need to check whether this is true or not. The way we can do this is by representing both numbers in the same way. This makes them easier to compare. What if we wrote our first number using digits. To help us do this, let’s sketch out a place value grid. We’re going to need ones, tens, and hundreds.
Now, the number that we’re looking to represent using digits has five ones. So, let’s write a five in the ones place. And seven hundreds, so write a seven in the hundreds place. Now, our number doesn’t just look like this. We need to show that there’s an empty tens column, so we’ll put a zero in as a placeholder, 705. Now, that we’ve represented the number using digits, it’s a lot easier to compare it to 750.
First, let’s compare the hundreds digits. Both numbers have seven hundreds, so we need to keep going and this time compare the tens digits. Our first number has zero tens and the second number has five tens, and so we can say our first number is less than our second number. 705 is less than 750.
It’s perhaps easier to compare two numbers when they’re both written in digits. But it is possible to compare our numbers if they were both written using words. As we know, our first number is described as having five ones and seven hundreds. Now, it’s possible to write our second number as five of something else and seven hundreds.
Look where the five digit is. It’s in the tens column, five tens and seven hundreds. Now, five ones are less than five tens, so five ones and seven hundreds are going to be less than five tens and seven hundreds. So, whichever way we represent these numbers, the statement five ones and seven hundreds is greater than 750 is false.