### 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: 73.3 ≈ 73.333333333333333...

#### Our number is sitting on the axis of numbers between two 10 decimal place consecutive neighboring numbers:

73.3333333333 < 73.3 < 73.3333333334

#### 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: (73.3333333333 + 73.3333333334) ÷ 2 = 73.33333333335

#### Our number, 73.3 ≈ 73.333333333333333..., is smaller than 73.33333333335, so it is closer to the smaller neighbor: 73.3333333333

#### Except for 'To Ceiling, To Floor', the rounded off number (both the positive and the negative) will be equal only to this smaller 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 3: 73.333333333333333...

#### In a positive number, if the digit to the right of the 'rounding digit' is smaller than 5, then the number is rounded to the smaller neighbor.

#### The digit is 3: 73.333333333333333... ≈ 73.3333333333 rounded to the nearest ten billionth (10 decimal places).

#### Or, even simpler.

In any number rounded to decimal places, if the digit to the right of the 'rounding digit' is less than 5 (0 to 4), then leave the 'rounding digit' as it is and drop all the digits to the right of it:

#### 73.333333333333333... ≈ 73.3333333333 rounded to the nearest ten billionth (10 decimal places)

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

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

### Number Round Half Up:

#### Numbers that are halfway between two neighbors are rounded off to the larger neighbor. 73.3 is not halfway between its neighbors.

#### 73.3 ≈ 73.3333333333

#### - 73.3 ≈ - 73.3333333333

#### rounded to the nearest ten billionth (10 decimal places)

### Number Round Half Down:

#### Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 73.3 is not halfway between its neighbors.

#### 73.3 ≈ 73.3333333333

#### - 73.3 ≈ - 73.3333333333

#### rounded to the nearest ten billionth (10 decimal 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. 73.3 is not halfway between its neighbors.

#### 73.3 ≈ 73.3333333333

#### - 73.3 ≈ - 73.3333333333

#### rounded to the nearest ten billionth (10 decimal places)

### Number Round Half Towards Zero:

#### Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero. 73.3 is not halfway between its neighbors.

#### 73.3 ≈ 73.3333333333

#### - 73.3 ≈ - 73.3333333333

#### rounded to the nearest ten billionth (10 decimal 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. 73.3 is not halfway between its neighbors.

#### 73.3 ≈ 73.3333333333

#### - 73.3 ≈ - 73.3333333333

#### rounded to the nearest ten billionth (10 decimal 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. 73.3 is not halfway between its neighbors.

#### 73.3 ≈ 73.3333333333

#### - 73.3 ≈ - 73.3333333333

#### rounded to the nearest ten billionth (10 decimal places)

### Number Round Ceiling:

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

#### 73.3 ≈ 73.3333333334

#### - 73.3 ≈ - 73.3333333333

#### rounded to the nearest ten billionth (10 decimal places)

### Number Round Floor:

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

#### 73.3 ≈ 73.3333333333

#### - 73.3 ≈ - 73.3333333334

#### rounded to the nearest ten billionth (10 decimal places)

### More operations like this: