66,000 < 66,510 < 67,000

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:

(Gaussian Rounding or Banker's Rounding)

(Gaussian Rounding or Banker's Rounding)

- Rounding a number means replacing it by another value that is 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.

- Identify the place value of the digit to be rounded - this is called the rounding digit.
- Identify the next digit to the right of the rounding digit, if there is any:
- If there is no other digit to the right, then the number is not changing, it stays the same.
**Rounding down**. If there is a digit to the right of the rounding digit and this digit is less than 5 (ie: 0 to 4), then leave the rounding digit as it is and replace all the digits to the right of it with zeros. This is called rounding down.**Rounding up**. If there is a digit to the right of the rounding digit and this digit is 5 or more (ie: 5 to 9), then increase the rounding digit by 1 and replace all the digits to the right of it with zeros. This is called rounding up.

#### >> See in the article how to round off numbers to whole places, plus examples

- Identify the place value of the digit to be rounded - this is called the rounding digit and it is the last digit to keep.
- Identify the next digit to the right of the rounding digit, if there is any:
- If there is no other digit to the right, then the number is not changing, it stays the same.
**Rounding down**. If there is a digit to the right of the rounding digit and this digit is less than 5 (ie: 0 to 4), then leave the rounding digit as it is and drop all the decimal digits to the right of it. This is called rounding down.**Rounding up**. If there is a digit to the right of the rounding digit and this digit is 5 or more (ie: 5 to 9), then increase the rounding digit by 1 and drop all the decimal digits to the right of it. This is called rounding up.

#### >> See in the article how to round off numbers to decimal places, plus examples

- The next digit to the right of the rounding digit is 5 and it is also the last non-zero digit in that number.
- In these cases the numbers can either be rounded up or down, depending on the type of rounding, as shown below.
- Types of rounding:
#### 5.1. Number Round Half Up.

- Numbers that are halfway between two neighbors are rounded off to the larger neighbor.
#### >> See examples on numbers rounded half up

#### 5.2. Number Round Half Down.

- Numbers that are halfway between two neighbors are rounded off to the smaller neighbor.
#### >> See examples on numbers rounded half down

#### 5.3. 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.
#### >> See examples on numbers rounded half away from zero

#### 5.4. Number Round Half Towards Zero.

- Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero.
#### >> See examples on numbers rounded half towards zero

#### 5.5. 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.
#### >> See examples on numbers rounded half to even (Gaussian rounding or Banker's rounding)

#### 5.6. 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.
#### >> See examples on numbers rounded half to odd (Gaussian rounding or Banker's rounding)

#### 5.7. Number Round Ceiling.

- All the numbers that are between two neighbors are always rounded off to the larger neighbor.
#### >> See examples on numbers rounded half to ceiling

#### 5.8. Number Round Floor.

- All the numbers that are between two neighbors are always rounded off to the smaller neighbor.
#### >> See examples on numbers rounded half to floor