INEQUALITIES – WHOLE 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 whole numbers do not have the same number of digits, the whole number with the most digits is always greater.
Example | Compare 8674 and 567. | 8674 567
Step 1 | Count the number of digits in the first number. There are four digits in the first number. | 8 6 7 4 1 2 3 4
Step 2 | Count the number of digits in the second number. There are three digits in the second number. | 5 6 7 1 2 3
Step 3 | Compare the number of digits. Since there are four digits in the first number (8674) and three digits in the second number (567), the first number is greater than the second number. | 8674 567

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

| HINT: Consider the symbols for greater than and less than as arrows which always point to the smaller number.
Directive 2 | When two whole numbers have the same number of digits, compare the digits from left to right to determine which number is greater.
Example | Compare 567 and 578. | 567 578
Step 1 | Count the number of digits in the first number. There are three digits in 567. | 5 6 7 1 2 3
Step 2 | Count the number of digits in the second number. There are three digits in 578. | 5 7 8 1 2 3
Step 3 | Compare the number of digits. There are three digits in the first number (567) and three digits in the second number (578). | 5 6 7 5 7 8 1 2 3
Step 4 | Since both numbers have the same number of digits, compare the digits from left to right. The leftmost digit in both numbers is the same, 5. | 5 67 5 78
| Look one digit to the right of 5 and compare. The digit to the right of 5 in the number 5 6 7 is 6. The digit to the right of 5 in the number 5 7 8 is 7. 6 is less than 7. | 5 6 7 5 7 8
| Therefore, 567 is less than 578. | 567 < 578

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.