Rounding numbers is important when you want to preserve significant figures in calculations and to record long numbers. In everyday life, rounding is useful for calculating a tip or dividing the bill among diners when eating at a restaurant, or when you're estimating the amount of cash you'll need for a trip to the grocery store.

### Rules for Rounding Whole Numbers

When rounding numbers, you must first understand the term "rounding digit." When working with whole numbers and rounding to the closest 10, the* *rounding digit is the second number from the right—or the 10's place. When rounding to the nearest hundred, the third place from the right is the rounding digit—or the 100's place.

First, determine what your rounding digit is and then look to the digit at the right side.

- If the digit is 0, 1, 2, 3, or 4, do not change the rounding digit. All digits that are on the righthand side of the requested rounding digit become 0.
- If the digit is 5, 6, 7, 8, or 9, the rounding digit rounds up by one number. All digits that are on the righthand side of the requested rounding digit will become 0.

### Rounding Rules for Decimal Numbers

Determine what your rounding digit is and look to the right side of it.

- If that digit is 4, 3, 2, or 1, simply drop all digits to the right of it.
- If that digit is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of it.

Some teachers prefer another method, sometimes referred to as the "Banker's Rule," which provides more accuracy. When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e., round off to the nearest even digit). Following this rule, 2.315 and 2.325 both round to 2.32—instead of 2.325 rounding up to 2.33—when rounded off to the nearest 100th. The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.

### Examples of How to Round Numbers

765.3682 becomes:

- 1,000 when rounding to the nearest 1,000
- 800 when rounding to the nearest 100
- 770 when rounding to the nearest 10
- 765 when rounding to the nearest one (1)
- 765.4 when rounding to the nearest 10th
- 765.37 when rounding to the nearest 100th
- 765.368 when rounding to the nearest (1,000th)

Rounding comes in handy when you are about to leave a tip at a restaurant. Let's say your bill is $48.95. One rule of thumb is to round to $50 and leave a 15 percent tip. To quickly figure out the tip, say that $5 is 10 percent, and to reach 15 percent you need to add half of that, which is $2.50, bringing the tip to $7.50. If you want to round up again, leave $8—if the service was good, that is.