# Approximate number

An approximate number is a number that is close but not exactly equal to another number. It is the counterpart to exact numbers. There is no uncertainty in an exact number, while the definition of an approximate number is one in which uncertainty exists.

One way to think of approximate numbers is as numbers that arise through measurement or calculation. An exact number on the other hand, can be thought of as one that arises from counting. For example, there are 4 clovers on a four-leaf clover. 4 is an exact number. If the leaf of a four-leaf clover measured 7 cm, the 7 cm is an approximate number. This is because the measured length, while closer to 7 cm than it is to 7.1 cm or 7.2 cm, is still only an approximate measure. There is no way to exactly measure the length of the leaf. With highly precise tools, the measured value can be very close to the exact value, but we can never be certain that the measured value is exact.

Example

Chad saw a sign at the grocery store that stated: 3 candy bars for \$1.00. At this rate, what was the cost of each candy bar?

\$1.00 ÷ 3 = 0.3, where the line over the 3 indicates that it repeats indefinitely. This means that the real value is somewhere between \$0.33 and \$0.34, since 0.3 cannot be expressed exactly in decimals. Both \$0.33 and \$0.34 are approximate numbers for the exact cost of each bar. It is not possible to charge Chad \$0.3, so instead we could say that he was charged \$0.33 for two candy bars, and \$0.34 for the third candy bar.

## Rounding

There are many different ways to round numbers. Rounding to an integer, as we did above, is the most common.

### Rounding down to an integer

Rounding down to an integer is referred to as taking the floor, which means rounding towards negative infinity.

25.9 → 25

-25.1 → -26

Half values are rounded towards negative infinity.

25.5 → 25

-25.5 → -26

### Rounding up to an integer

Rounding up to an integer is referred to as taking the ceiling which means rounding towards positive infinity.

25.1 → 26

-25.9 → -25

Half values are rounded towards infinity.

25.5 → 26

-25.5 → -25

### Rounding towards zero

Rounding towards zero is referred to as truncating, which means rounding away from infinity.

25.9 → 25

-25.1 → -25

Half values are rounded away from infinity.

25.5 → 25

-25.5 → -25

### Rounding away from zero

Rounding away from zero means rounding towards infinity.

25.1 → 26

-25.1 → -26

Half values are rounded towards infinity.

25.5 → 26

-25.5 → -26

There are also other rounding methods, but these are some of the most common.