INEQUALITIES – DECIMAL NUMBERS

Concept: In an inequality, two unequal numbers are compared to determine which is larger and which is smaller. Follow the Directives below to make that determination.

Directive 1 | When two decimals have the same number of digits, compare the digits in both decimals, moving from left to right, to determine which decimal is greater.
Example | Compare 0.345 and 0.323. | 0.345 0.323
Compare the digits in both decimals, moving from left to right, to determine which decimal is greater. The leftmost digit in both numbers is the same, 3. | 0.3 45 0.3 23
Look one digit to the right of 3 and compare. The digit to the right of 3 in the number 0.3 4 5 is 4. The digit to the right of 3 in the number 0.3 2 3 is 2. 2 is less than 4. | 0.3 4 5 0.3 2 3
Therefore, 0.3 2 3 is less than 0.3 4 5. | 0.323<0.345

| HINT: Consider the symbols for greater than and less than as arrows which always point to the smaller number.
Directive 2 | When two decimals have a different number of digits, compare the digits in each decimal, moving from left to right, to determine which decimal is greater.
Example | Compare 0.354657 and 0.353. | 0.354657 0.353
Compare the digits in each decimal from left to right to determine which decimal is larger. The leftmost digit in both numbers is the same, 3. | 0.3 54657 0.3 53
Look one digit to the right of 3 and compare. The digit to the right of 3 in the number 0.3 5 4657 is 5. The digit to the right of 3 in the number 0.3 5 3 is 5, so they are the same. | 0.3 5 4657 0.3 5 3
Look one digit to the right of 5 and compare. The digit to the right of 5 in the number 0.3 5 4 657 is 4. The digit to the right of 5 in the number 0.3 5 3 is 3. 3 is less than 4. | 0.3 5 4 657 0.3 5 3
Therefore, 0.3 5 3 is less than 0.3 5 4 657. | 0.353 <0.354657

Use the following symbols to express number comparisons.

= | means equals | .234 = .234 | .234 equals .234
> | means greater than | .55 > .3 2 | .55 is greater than .32
< | means less than | .23 < .66 | .23 is less than .66

Directive 3 | When dealing with signed numbers, the number farthest to the left on a number line is the smaller number.

Example Compare – 8 and – 4. Since – 8 is further to the left on the number line than – 4 is, – 8 < – 4.