Question Video: Comparing Two Decimals with the Same Number of Decimal Places Using Place Value Counters

Complete the following using >, <, or =.

03:15

Video Transcript

Complete the following using the symbol for is greater than, is less than, or is equal to.

An abacus is a way of modeling a number. And in this question, we’ve got two to look at. We need to compare both numbers together and then choose the correct symbol to show whether the first number is greater than the second, whether it’s less than the second number, or whether the two numbers are exactly the same. Our first number shows two ones and three-tenths. It’s a decimal number. We know this because it’s made up of a whole part — two ones or a whole number — but also a fractional part. That’s a part that’s worth less than one. And three-tenths of this fractional part, three-tenths are less than one.

And if we were to write this number using digits, we need a two in the ones place, then a decimal point to show that we’re moving into the fractional part, and then a three in the tenth place. Two ones and three-tenths is the same as 2.3. Now let’s look at our second number. This is made up of one one and seven-tenths. So we have less ones, but a few more tenths in this number. And again, it’s a decimal. This is because it’s made up of that whole part and a part that’s worth less than one. This time, we could represent this model using digits with a one in the ones place. Again, we’re going to need a decimal point to separate it from the fraction part and then a seven in the tenths place to show our seven-tenths. One and seven-tenths is the same as 1.7.

So how are we going to compare these two decimals that have been modeled on each abacus? Should we compare the number of beads in the tenths place first? Or should we think about the ones? Well, we need to apply the same rule that we use when we compare whole numbers. And that’s to compare the digits that have the largest value first and work our way from left to right. So we shouldn’t start by comparing the tenths. A tenth is less than one. We need to start by looking at the number of ones that we have.

Our first abacus shows two in the ones place, but, in our second abacus, there’s only one bead in the ones place. It doesn’t matter how many tenths each number has, because we’ve compared the ones. And we can see that the first number is larger than the second. 2.3 or two ones and three-tenths is greater than 1.7 or one one and seven-tenths. The correct symbol to use in between these two models is the one that represents is greater than.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.