Question Video: Comparing Two Decimals with the Same Number of Decimal Places Using a Place Value Table | Nagwa Question Video: Comparing Two Decimals with the Same Number of Decimal Places Using a Place Value Table | Nagwa

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

Complete the following using =, <, or >.

03:47

Video Transcript

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

In this question, we’re given two numbers, and they’ve been written for us in place value tables. Let’s read them. Our first number contains one one, four-tenths, and eight hundredths, 1.48. Our second number also has a single one, it also has four-tenths, but this time it has six hundredths, 1.46. These two numbers are decimals. They have a whole part. That’s the number of ones. But then they also have a part that’s worth less than one. And to separate the whole part from the fractional part, we use a decimal point.

Now, in between our two decimals, there’s a box. And we need to complete the statement using one of the comparison symbols we’re given equal to, less than, or greater than. In other words, we need to compare both these decimals together. Now both of these decimals have been written in place value tables to help us. So we can compare them digit by digit. Now shall we start with the hundredths and work from right to left? Or shall we start with the ones and work from left to right? Well, if we take a moment to think about what each one of these columns is worth, we know that our ones column represents one whole.

Now, as we move to the right, each new column is worth 10 times less than the one before. So a tenth is 10 times less than a whole. It’s what we get if we take a whole and split it up into 10 equal parts. And then a hundredth is 10 times less again. It’s what we get if we take one of our tenths and split that up into 10 equal parts. So knowing that, which part of our number do you think is most important? It’s the part that’s worth the most. We need to start by comparing our ones column and then work from left to right. Our first decimal number contains a one in the ones place. But can you see we’ve also got this in our second number too? So we can’t separate our numbers just by looking at the ones. We’re going to need to move on and look at the tenths.

Both numbers have a four in the tenths place. We still can’t separate them. The beginning of both our decimals is the same, isn’t it, one and four-tenths. We’re going to need to compare the hundredth digits. Below these are the digits that have the least value in our numbers. They’re actually going to turn out to be the ones that make the difference. This tells us that the difference or a gap between our two numbers is very small. It’s just going to be a matter of hundredths. Our first number has an eight in the hundredths place, but our second number only has a six. And eight hundredths are greater than six hundredths.

The difference between our two numbers is only two hundredths, which is a tiny difference. But it’s enough for us to be able to say which number is larger. We’ve compared these two decimal numbers digit by digit using place value tables. One, four tenths, and eight hundredths is greater than one, four tenths, and six hundredths. Or to say it a different way, 1.48 is greater than 1.46. The correct symbol to use in between these two decimals is the one that represents is greater than.

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