### 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: 9.5 ≈ 9.555555555555555...

#### Our number is sitting on the axis of numbers between two 1 decimal place consecutive neighboring numbers:

9.5 < 9.5 < 9.6

#### 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: (9.5 + 9.6) ÷ 2 = 9.55

#### Our number, 9.5 ≈ 9.555555555555555..., is larger than 9.55, so it is closer to the larger neighbor: 9.6

#### 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 5: 9.555555555555555...

#### 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: 9.555555555555555... ≈ 9.6 rounded to the nearest tenth (1 decimal place).

#### Or, even simpler.

In any number rounded to decimal 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 drop all the digits to the right of it, 5 + 1 = 6:

#### 9.555555555555555... ≈ 9.6 rounded to the nearest tenth (1 decimal 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. 9.5 is not halfway between its neighbors.

#### 9.5 ≈ 9.6

#### - 9.5 ≈ - 9.6

#### rounded to the nearest tenth (1 decimal place)

### Number Round Half Down:

#### Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 9.5 is not halfway between its neighbors.

#### 9.5 ≈ 9.6

#### - 9.5 ≈ - 9.6

#### rounded to the nearest tenth (1 decimal 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. 9.5 is not halfway between its neighbors.

#### 9.5 ≈ 9.6

#### - 9.5 ≈ - 9.6

#### rounded to the nearest tenth (1 decimal place)

### Number Round Half Towards Zero:

#### Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero. 9.5 is not halfway between its neighbors.

#### 9.5 ≈ 9.6

#### - 9.5 ≈ - 9.6

#### rounded to the nearest tenth (1 decimal 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. 9.5 is not halfway between its neighbors.

#### 9.5 ≈ 9.6

#### - 9.5 ≈ - 9.6

#### rounded to the nearest tenth (1 decimal 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. 9.5 is not halfway between its neighbors.

#### 9.5 ≈ 9.6

#### - 9.5 ≈ - 9.6

#### rounded to the nearest tenth (1 decimal place)

### Number Round Ceiling:

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

#### 9.5 ≈ 9.6

#### - 9.5 ≈ - 9.5

#### rounded to the nearest tenth (1 decimal place)

### Number Round Floor:

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

#### 9.5 ≈ 9.5

#### - 9.5 ≈ - 9.6

#### rounded to the nearest tenth (1 decimal place)

### More operations like this: