### What does it mean to round off a number?

#### Rounding a number means replacing it with a simpler, shorter approximation, while keeping its value close to the initial one. The rounded number will be less accurate, but easier to work with.

### How is the number rounded off? Explanation.

#### Counting by units (1 whole place at a time), our number is sitting on the axis of numbers between two consecutive neighboring numbers:

8 < 8.5 < 9

#### Our number is to be rounded off to one of these neighbors, the closer one.

#### The middle of this interval, the number that is equally close to the either neighbor, is: (8 + 9) ÷ 2 = 8.5

#### Our number, 8.5, is equal to the middle of the interval, so it is equally close to the either neighbor. The number will be rounded either to 8 or to 9, depending on the type of rounding below.

### Rule of thumb:

#### Rounding digit. Let's call the digit of the position place that is intended to round off to as the 'rounding digit'. The digit is 8: 8.5

#### If the digit to the right of the 'rounding digit' is equal to 5 and it is the last non-zero digit to the right, then the number will be rounded either to the smaller or to the larger neighbor, depending on the type of rounding.

#### The digit is 5: 8.5 ≈ 8 or 8.5 ≈ 9 rounded to the nearest one (1 whole place).

#### Or, even simpler.

In any number rounded to whole places, if the digit to the right of the 'rounding digit' is 5 and it is the last non-zero digit to the right, then either increase the 'rounding digit' by 1 or leave it unchanged, but don't forget to replace all the digits to the right of it with zeros:

#### 8.5 ≈ 9 or 8.5 ≈ 8 rounded to the nearest one (1 whole place).

### Below we round off both the positive and the negative:

#### Half Up, Half Down, Half Away From Zero, Half Towards Zero, Half to Even, Half to Odd. To Ceiling, To Floor.

### Number Round Half Up:

#### Numbers that are halfway between two neighbors are rounded off to the larger neighbor. 8.5 is halfway between its neighbors.

#### 8.5 ≈ 9

#### - 8.5 ≈ - 8

#### rounded to the nearest one (1 whole place)

### Number Round Half Down:

#### Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 8.5 is halfway between its neighbors.

#### 8.5 ≈ 8

#### - 8.5 ≈ - 9

#### rounded to the nearest one (1 whole place)

### Number Round Half Away From Zero:

#### Numbers that are halfway between two neighbors are rounded off to the neighbor which is farther away from zero. 8.5 is halfway between its neighbors.

#### 8.5 ≈ 9

#### - 8.5 ≈ - 9

#### rounded to the nearest one (1 whole place)

### Number Round Half Towards Zero:

#### Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero. 8.5 is halfway between its neighbors.

#### 8.5 ≈ 8

#### - 8.5 ≈ - 8

#### rounded to the nearest one (1 whole place)

### Number Round Half to Even:

(Gaussian Rounding or Banker's Rounding)

#### Numbers that are halfway between two neighbors are rounded off to the neighbor with an even rounding digit. 8.5 is halfway between its neighbors.

#### 8.5 ≈ 8

#### - 8.5 ≈ - 8

#### rounded to the nearest one (1 whole place)

### Number Round Half to Odd:

(Gaussian Rounding or Banker's Rounding)

#### Numbers that are halfway between two neighbors are rounded off to the neighbor with an odd rounding digit. 8.5 is halfway between its neighbors.

#### 8.5 ≈ 9

#### - 8.5 ≈ - 9

#### rounded to the nearest one (1 whole place)

### Number Round Ceiling:

#### All the numbers that are between two neighbors are always rounded off to the larger neighbor.

#### 8.5 ≈ 9

#### - 8.5 ≈ - 8

#### rounded to the nearest one (1 whole place)

### Number Round Floor:

#### All the numbers that are between two neighbors are always rounded off to the smaller neighbor.

#### 8.5 ≈ 8

#### - 8.5 ≈ - 9

#### rounded to the nearest one (1 whole place)

### More operations like this: