## How to Compare Decimal Numbers

We have already learned how to **compare fractions** and in this post, we are going to learn how to compare decimals. In comparing decimals it is important to understand place value. In the number 213.489, the following are their place values. For the whole numbers,

2 – hundred

1 – tens

3 – ones.

For the decimal numbers,

4 – tenths

8 – hundredths

9 – thousandths

In whole numbers, clearly, the larger the number of digits the larger the number. For example, 821 > 92 since 821 has three digits and 92 has only two digits. Since whole numbers are always greater than decimal numbers in comparing decimal numbers, look at the whole numbers first. Therefore, we have the following rule.

**Rule 1:** In comparing decimal numbers, look at the whole number first. The decimal numbers containing larger whole numbers have larger values.

Example 1: 84.23 > 82.345 since 84 is greater than 82.

Example 2: 12.56 < 15.001 since 12 is less than 15.

Example 3: 141.85 > 123.4 because 141 is greater than 123

**Rule 2:** If the whole numbers are equal, then compare the numbers by looking at the tenths place first. The number with the larger digit in tenths place is larger.

Example 1: 18.34 > 18.21 since 3 > 2.

Example 2: 12.95 > 12.15 since 9 > 1.

Example 3: 0. 9 > 0.873 since 9 > 8.

Notice that in Rule 2 Example 3, even if 0.873 has more digits, it is still less than 0.9 since 9 is greater than 8 and they are in the tenths place.

**Rule 3:** If the whole numbers and the tenths place are equal, then compare first the hundredths place. The number with the larger digits in the hundredths place is the larger number.

Rules 2 and 3 can be generalized. That means that you have to compare the digits from the tenths place first, then hundredths, then thousandths, and so on.

**What about negative numbers?**

Please take note however the rules of negative numbers.

- Positive numbers are always greater than negative numbers.
- If both numbers are negative, do the following:

1.) Make them positive

2.) Apply the rules above

3.) Reverse your answer.

Example: Compare -82.45 and -82.31

1.) Make them positive: 82.45 and 82.31

2.) Apply the rules above:

From the rules above, the whole numbers are both 82, so we look at the tenths place. 0.4 > 0.3, so 82.45 > 82.31

3.) Reverse the answer. Since 82.45 > 82.31, – 82.31 > – 82.45.