Inequalities with decimals
key notes:
Comparing decimals means determining which decimal represents a larger number, and which represents a smaller number.
Ordering decimals means putting them in order from the least to the greatest, or from the greatest to the least.
| = | When two values are equal, we use the “equals” sign | example: 0.2+0.2 = 0.4 |
|---|---|---|
| < | When one value is smaller than another, we can use a “less than” sign. | example: 0.3 < 0.5 |
| > | When one value is bigger than another, we can use a “greater than” sign | example: 0.9 > 0.6 |
How to Tell Which Decimal is Bigger
When given two decimal numbers, how can someone tell which decimal is bigger? The process is similar to what is done when words are alphabetized. If the first letter of each word is the same, look at the second letter. If the second letter is the same, look at the third letter. Here is how to tell which decimal number is bigger:
- Write the numbers with the decimal points lined up.
- Starting at the far left, which is the largest place value, compare the numbers.
- If the first place value is the same in both numbers, move one spot to the right and compare again.
- If the second place value is the same in both numbers, move one spot to the right and compare again.
- Continue until the place value digits are different. The number with the larger digit is the larger number.
Here is an example.
Which number is bigger, 8.019 or 8.03?
Follow the steps:
- Write the numbers with the decimal points lined up.
| 8 | . | 0 | 1 | 9 |
| 8 | . | 0 | 3 |
- Starting at the far left, which is the largest place value, compare the numbers.
The digit in the ones place in both numbers is an 8.
- If the first place value is the same in both numbers, move one spot to the right and compare again.
The digit in the tenths place in both numbers is a 0.
- If the second place value is the same in both numbers, move one spot to the right and compare again.
The digit in the hundredths place in the top number is a 1, and it is a 3 in the bottom number.
- The number with the larger digit is the larger number.
Since 3 is bigger than 1, then 8.03 > 8.019
8.03 > 8.019
Learn with an example
Which sign makes the statement true?
0.011? 0.811
- >
- <
Use a place value chart. Be sure to line up the decimal points.
Compare the digits, starting with the highest place value. The ones digits are the same. The tenths digits are different. The tenths digit in 0.011 is less than the tenths digit in 0.811.
0.011 is less than 0.811.
Use the less-than sign.
0.011 < 0.811
Which sign makes the statement true?
0.68 ? 0.63
- >
- <
Use a place value chart. Be sure to line up the decimal points.
Compare the digits, starting with the highest place value. The ones and tenths digits are the same. The hundredths digits are different. The hundredths digit in 0.68 is greater than the hundredths digit in 0.63.
0.68 is greater than 0.63.
Use the greater-than sign.
0.68 > 0.63
Which sign makes the statement true?
0.5 ? 0.7
- >
- <
Use a place value chart. Be sure to line up the decimal points.
| ones | tenths | |
| 0 | . | 5 |
| 0 | . | 7 |
Compare the digits, starting with the highest place value. The ones digits are the same. The tenths digits are different. The tenths digit in 0.5 is less than the tenths digit in 0.7.
0.5 is less than 0.7.
Use the less-than sign.
0.5 < 0.7
let’s practice:
