# 8.196: Round off the (terminating) decimal number to the nearest one (1 whole place)

## The latest 13 operations with rounded off numbers:

 Round off 8.196 to the nearest one (1 whole place) Dec 02 00:00 UTC (GMT) Round off 124,027 to the nearest ten thousand (5 whole places) Dec 01 23:59 UTC (GMT) Round off 110,504.2 to the nearest hundredth (2 decimal places) Dec 01 23:59 UTC (GMT) Round off 303.5 to the nearest ten (2 whole places) Dec 01 23:59 UTC (GMT) Round off 2.4 to the nearest ten thousandth (4 decimal places) Dec 01 23:58 UTC (GMT) Round off 5,075 to the nearest hundred (3 whole places) Dec 01 23:58 UTC (GMT) Round off 1.1398 to the nearest hundredth (2 decimal places) Dec 01 23:58 UTC (GMT) Round off 5,437 to the nearest thousand (4 whole places) Dec 01 23:58 UTC (GMT) Round off 0.346 to the nearest hundredth (2 decimal places) Dec 01 23:58 UTC (GMT) Round off 80.1 to the nearest ten (2 whole places) Dec 01 23:57 UTC (GMT) Round off 926,044,277 to the nearest hundred thousand (6 whole places) Dec 01 23:57 UTC (GMT) Round off 17.8 to the nearest hundredth (2 decimal places) Dec 01 23:57 UTC (GMT) Round off 218.4 to the nearest hundred (3 whole places) Dec 01 23:57 UTC (GMT) All the operations with the numbers rounded off by users...

## How to round off numbers?

### 1. Rounding off numbers: definition.

• 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.

### 2. How to round off a number to whole places?

• 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.

### 3. How to round off a number to decimal places?

• 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.

### 5. Special cases. 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.

• #### 5.2. Number Round Half Down.

• Numbers that are halfway between two neighbors are rounded off to the smaller neighbor.

• #### 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.

• #### 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.

• #### 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.

• #### 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.

• #### 5.7. Number Round Ceiling.

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

• #### 5.8. Number Round Floor.

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