0.0101010401216: Round off the mixed repeating (recurring) decimal number to the nearest tenth (1 decimal place)

0.0101010401216 rounded to the nearest tenth (1 decimal place) = ?

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: 0.0101010401216 ≈ 0.010101040121610401216...


Our number is sitting on the axis of numbers between two 1 decimal place consecutive neighboring numbers:
0 < 0.0101010401216 < 0.1


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: (0 + 0.1) ÷ 2 = 0.05


Our number, 0.0101010401216 ≈ 0.010101040121610401216..., is smaller than 0.05, so it is closer to the smaller neighbor: 0


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 0: 0.010101040121610401216...

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 1: 0.010101040121610401216... ≈ 0 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 less than 5 (0 to 4), then leave the 'rounding digit' as it is and drop all the digits to the right of it:

0.010101040121610401216... ≈ 0 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. 0.0101010401216 is not halfway between its neighbors.


0.0101010401216 ≈ 0


- 0.0101010401216 ≈ 0


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. 0.0101010401216 is not halfway between its neighbors.


0.0101010401216 ≈ 0


- 0.0101010401216 ≈ 0


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. 0.0101010401216 is not halfway between its neighbors.


0.0101010401216 ≈ 0


- 0.0101010401216 ≈ 0


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. 0.0101010401216 is not halfway between its neighbors.


0.0101010401216 ≈ 0


- 0.0101010401216 ≈ 0


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. 0.0101010401216 is not halfway between its neighbors.


0.0101010401216 ≈ 0


- 0.0101010401216 ≈ 0


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. 0.0101010401216 is not halfway between its neighbors.


0.0101010401216 ≈ 0


- 0.0101010401216 ≈ 0


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.


0.0101010401216 ≈ 0.1


- 0.0101010401216 ≈ 0


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.


0.0101010401216 ≈ 0


- 0.0101010401216 ≈ - 0.1


rounded to the nearest tenth (1 decimal place)


More operations like this:

0.0101010401217: Round off the mixed repeating (recurring) decimal number to the nearest tenth (1 decimal place)


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:

Round off 0.0101010401216 to the nearest tenth (1 decimal place) Feb 12 20:42 UTC (GMT)
Round off 48.11111177112533 to the nearest ten (2 whole places) Feb 12 20:42 UTC (GMT)
Round off 2.71828182869858 to the nearest ten millionth (7 decimal places) Feb 12 20:42 UTC (GMT)
Round off 6.36363636497486 to the nearest hundredth (2 decimal places) Feb 12 20:42 UTC (GMT)
Round off 0.0101263675154 to the nearest ten billiardth (13 decimal places) Feb 12 20:42 UTC (GMT)
Round off 0.01010106010856 to the nearest tenth (1 decimal place) Feb 12 20:42 UTC (GMT)
Round off 0.010175151 to the nearest ten billiardth (13 decimal places) Feb 12 20:42 UTC (GMT)
Round off 0.01010107388758 to the nearest billiardth (12 decimal places) Feb 12 20:42 UTC (GMT)
Round off 48.11111639132526 to the nearest tenth (1 decimal place) Feb 12 20:42 UTC (GMT)
Round off 0.010175151 to the nearest ten billiardth (13 decimal places) Feb 12 20:42 UTC (GMT)
Round off 33.111151347 to the nearest hundredth (2 decimal places) Feb 12 20:42 UTC (GMT)
Round off 48.11111639132526 to the nearest tenth (1 decimal place) Feb 12 20:42 UTC (GMT)
Round off 0.01010107388758 to the nearest billiardth (12 decimal places) Feb 12 20:42 UTC (GMT)
All the operations with the numbers rounded off by users...

How to round off numbers?

1. Rounding off numbers: definition.

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

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

4. Mathematical explanation of the rules used in numbers rounding.

5. Special cases. Examples.