Arrange the numbers 197, 971, 791, 179, 917 to complete the following.
The first thing we notice about the order they are asking us to put these numbers in is that we’re using all “less than” symbols, which means the digit on the far left will be the smallest. And from left to right, we’ll move to the largest value. This question is asking us to arrange five digits from least to greatest. To do this I’m gonna stack numbers on top of each other in a line. Starting with 197, next up 971, then we have 791, 179, and finally 917.
To compare these values, we’ll start by comparing the largest place values, the digits in the largest place values. In our case, those digits fall in the hundreds place. And remember, while we’re comparing, we’re looking for the smallest. So let’s look for the smallest digit in the hundreds column.
In the hundreds column, we have two numbers that have one in the hundreds place. Since those values are the same — they’re the smallest, but they’re the same — we’ll need to check the tens place on these values. Again remember that we’re looking for the smallest value, so our first row has one and then a nine. Our second number we’re looking at has a one and then a seven.
Seven is smaller than nine, so 179 would be smaller than 197, which makes 179 the smallest value and the first value we would write down. After that, we can go ahead and write 197 because it’s the second smallest. Now that we’ve used 179 and 197, we’ll cross these two values out and we’ll look for the next smallest hundreds value. The next smallest hundreds value is a seven, the number 791 would be the next highest value.
As we look back at our hundreds again, we see that we have two nines. Our hundreds place is not going to help us compare. We’ll need to move to the tens place. Comparing the tens place for each of these values, we see we have a seven and a one. The one is smaller than the seven, which means 917 is less than 971. 917 comes next in our ordering; we cross that out, leaving us with 971 as our largest value.
From smallest to largest, our values are 179, 197, 791, 917, and 971.