Decimals
13 Compare and Round Decimals
Compare Decimals
Chad wants to make sure that all his students understand the value of money, and an important aspect of that is knowing how to accurately determine the sizes of decimals. Take a look at the following four decimals.
- 8.16
- 8.151
- 8.1513
- 8.15138
Which of these is the largest? To answer the question, you would have to compare decimals.
At first glance, you might say the largest number is 8.15138, as it has the most digits and may look like the largest. But if we referred back to the chapter on Understanding Decimal Notation, we would remember that, as you go further to the right from the decimal point (.), the numbers become smaller. So in the example 8.15138, the 3 near the end is worth far less than the 5 two spots to the left of the decimal point.
If we followed this logic, then the largest number of the four would be 8.16, even though it has the fewest digits. When comparing decimals, we really have to start with the whole number. In this situation, it’s 8 in all four answers, so it doesn’t come into play.
Once we have decided that the whole number is equal in all four cases, the next thing we have to look at is the number directly to the right of the decimal. This is the tenths place and is worth the most in decimals. Once again, all four answers give us a value of 1 in the tenths column, so this will not be the determining factor. Move one space to the right again and you get the hundredths place. All the numbers contain a 5, except the first number, where we have a 6. Therefore, this is the defining place value.
I’ll go through another example, and then you can try a couple on your own.
Example
Which of the following is the largest number?
- 7.34
- 7.332
- 7.323
- 7.3234
Following the same pattern as before, we would go through the following steps.
Step 1: Start with the whole number. Which number has the largest whole number? As they are all equal, this will not be the determining factor.
The whole number in all four cases is a 7. This is not the deciding factor.
Step 2: Go to the first digit to the right of the decimal. It works out that the digit is a 3 in all cases. Therefore, this is not the deciding factor, either.
The number in the tenths column in all four cases is a 3. This is not the deciding factor.
Step 3: Go one place to the right again. This would be the hundredths place. Here, we find the first difference. Answer a gives us the largest number in this column. Therefore, answer a is the largest number.
The digit in the hundredths column is different for each number. In this case, the number with the highest value in the hundredths column is the largest number.
Therefore, the largest number of the four is:
[latex]\LARGE7.34[/latex]
Practice Questions
Now try a couple for yourself and check out the video answers.
Find the largest number.
Question 1
- 27.5
- 27.54
- 27.539
- 27.5392
Question 2
- 14.001
- 13.099
- 13.999
- 13.001
Rounding Decimals
During the course, Chad ta