1,456.7890123489892: Round off the mixed repeating (recurring) decimal number to the nearest hundredth (2 decimal places)
1,456.7890123489892 rounded to the nearest hundredth (2 decimal places) = ?
How is the number rounded off? Half Up, Half Down, Half Away From Zero, Half Towards Zero, Half to Even, Half to Odd. To Ceiling, To Floor.
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: 1,456.7890123489892 ≈ 1,456.7890123489892123489892...
Our number is sitting on the axis of numbers between two 2 decimal place consecutive neighboring numbers:
1,456.78 < 1,456.7890123489892 < 1,456.79
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: (1,456.78 + 1,456.79) ÷ 2 = 1,456.785
Our number, 1,456.7890123489892 ≈ 1,456.7890123489892123489892..., is larger than 1,456.785, so it is closer to the larger neighbor: 1,456.79
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 8: 1,456.7890123489892123489892...
In a positive number, if the digit to the right of the 'rounding digit' is larger than 5, then the number is rounded to the larger neighbor.
The digit is 9: 1,456.7890123489892123489892... ≈ 1,456.79 rounded to the nearest hundredth (2 decimal places).
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, 8 + 1 = 9:
1,456.7890123489892123489892... ≈ 1,456.79 rounded to the nearest hundredth (2 decimal 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. 1,456.7890123489892 is not halfway between its neighbors.
1,456.7890123489892 ≈ 1,456.79
- 1,456.7890123489892 ≈ - 1,456.79
rounded to the nearest hundredth (2 decimal places)
Number Round Half Down:
Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 1,456.7890123489892 is not halfway between its neighbors.
1,456.7890123489892 ≈ 1,456.79
- 1,456.7890123489892 ≈ - 1,456.79
rounded to the nearest hundredth (2 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. 1,456.7890123489892 is not halfway between its neighbors.
1,456.7890123489892 ≈ 1,456.79
- 1,456.7890123489892 ≈ - 1,456.79
rounded to the nearest hundredth (2 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. 1,456.7890123489892 is not halfway between its neighbors.
1,456.7890123489892 ≈ 1,456.79
- 1,456.7890123489892 ≈ - 1,456.79
rounded to the nearest hundredth (2 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. 1,456.7890123489892 is not halfway between its neighbors.
1,456.7890123489892 ≈ 1,456.79
- 1,456.7890123489892 ≈ - 1,456.79
rounded to the nearest hundredth (2 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. 1,456.7890123489892 is not halfway between its neighbors.
1,456.7890123489892 ≈ 1,456.79
- 1,456.7890123489892 ≈ - 1,456.79
rounded to the nearest hundredth (2 decimal places)
Number Round Ceiling:
All the numbers that are between two neighbors are always rounded off to the larger neighbor.
1,456.7890123489892 ≈ 1,456.79
- 1,456.7890123489892 ≈ - 1,456.78
rounded to the nearest hundredth (2 decimal places)
Number Round Floor:
All the numbers that are between two neighbors are always rounded off to the smaller neighbor.
1,456.7890123489892 ≈ 1,456.78
- 1,456.7890123489892 ≈ - 1,456.79
rounded to the nearest hundredth (2 decimal places)
More operations like this:
All Numbers Are Rounded Off: Half Up, Half Down, Half Away From Zero, Half Towards Zero, Half to Even, Half to Odd. To Ceiling, To Floor. Rounding Off Integers, Terminating Decimals, Pure or Mixed Repeating (Recurring) Decimal Numbers
Round off to whole places or decimal places
The latest 13 operations with rounded off numbers:
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.
4. Mathematical explanation of the rules used in numbers rounding.
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.