### 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.

#### A repeating decimal has a number of decimals that repeat over and over again, infinitely: 545.8638 ≈ 545.8638383838383838...

#### Counting by tens (2 whole places at a time), our number is sitting on the axis of numbers between two consecutive neighboring numbers:

540 < 545.8638 < 550

#### 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: (540 + 550) ÷ 2 = 545

#### Our number, 545.8638 ≈ 545.8638383838383838..., is larger than 545, so it is closer to the larger neighbor: 550

#### Except for 'To Ceiling, To Floor', the rounded off number (both the positive and the negative) will be equal only to this larger neighbor.

### 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 4: 545.8638383838383838...

#### In a positive number, if the digit to the right of the 'rounding digit' is equal to 5 and it is not the last digit that is different from zero, then the number is rounded to the larger neighbor.

#### The digit is 5: 545.8638383838383838... ≈ 550 rounded to the nearest ten (2 whole places).

#### Or, even simpler.

In any number rounded to whole places, if the digit to the right of the 'rounding digit' is 5 (but it is not the last non-zero digit to the right) or more than 5, ie. 6, 7, 8 or 9, then increase the 'rounding digit' by 1 and replace all the digits to the right of it with zeros:

#### 545.8638383838383838... ≈ 550 rounded to the nearest ten (2 whole places)

### 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. 545.8638 is not halfway between its neighbors.

#### 545.8638 ≈ 550

#### - 545.8638 ≈ - 550

#### rounded to the nearest ten (2 whole places)

### Number Round Half Down:

#### Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 545.8638 is not halfway between its neighbors.

#### 545.8638 ≈ 550

#### - 545.8638 ≈ - 550

#### rounded to the nearest ten (2 whole places)

### 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. 545.8638 is not halfway between its neighbors.

#### 545.8638 ≈ 550

#### - 545.8638 ≈ - 550

#### rounded to the nearest ten (2 whole places)

### Number Round Half Towards Zero:

#### Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero. 545.8638 is not halfway between its neighbors.

#### 545.8638 ≈ 550

#### - 545.8638 ≈ - 550

#### rounded to the nearest ten (2 whole places)

### 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. 545.8638 is not halfway between its neighbors.

#### 545.8638 ≈ 550

#### - 545.8638 ≈ - 550

#### rounded to the nearest ten (2 whole places)

### 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. 545.8638 is not halfway between its neighbors.

#### 545.8638 ≈ 550

#### - 545.8638 ≈ - 550

#### rounded to the nearest ten (2 whole places)

### Number Round Ceiling:

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

#### 545.8638 ≈ 550

#### - 545.8638 ≈ - 540

#### rounded to the nearest ten (2 whole places)

### Number Round Floor:

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

#### 545.8638 ≈ 540

#### - 545.8638 ≈ - 550

#### rounded to the nearest ten (2 whole places)

### More operations like this: