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The greatest integer function is one of the nonbinary functions that is frequently used in algebra and its applications. This function is a method of rounding numbers. When you “round” a number to its nearest integer or tenth or thousandth or thousand, and so on, you move up or down to get to the closer value. With the greatest integer function, it doesn’t matter how close, it matters in which direction.

When rounding numbers, you determine what digits need to be dropped and whether the target place value or number goes up by 1 or stays the same.

Suppose you want to round 3.667 to the nearest integer. The target number is the 3. Because the next digit, the 6, is greater than 5, you round the 3 up to 4 and eliminate the rest of the digits. You can replace them with 0 or, in this case, just keep the number 4. So, in rounded form, or .

What if you’re asked to round 1234.567 to the nearest hundred? The target number is the 2. The next digit down is 3, which is smaller than 5, so you leave the 2 as is and replace the 3 and the rest of the smaller digits with 0s. or .

Note: When the digit below the target digit is exactly 5, and nothing else, you round up.

The greatest integer function acts a bit differently than rounding. It’s similar in that the greatest integer function eliminates unwanted fractions or decimals, but the greatest integer function only goes in one direction: down. Or, if you already have an integer, the greatest integer leaves the number alone.

Q. Which is larger: 5.7 rounded to the nearest integer or [5.7]?

A. Rounding 5.7 to the nearest integer, you home in on the 7, which will be eliminated. Because 7 is larger than 5, you round up: or . Using the greatest integer function, . So, rounding gives you the larger value.

Q. Compare rounded to the nearest integer and .

A. Rounding to the nearest integer, you drop off the , because its decimal value is about 0.333, or less than half; so, rounds to 13. Applying the greatest integer function, . So the values are the same.

35 Round 146.95 to the nearest integer.

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