399.66386: Round off the mixed repeating (recurring) decimal number to the nearest thousand (4 whole places)

399.66386 rounded to the nearest thousand (4 whole 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: 399.66386 ≈ 399.66386386386386386...


Counting by thousands (4 whole places at a time), our number is sitting on the axis of numbers between two consecutive neighboring numbers:
0 < 399.66386 < 1,000


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 + 1,000) ÷ 2 = 500


Our number, 399.66386 ≈ 399.66386386386386386..., is smaller than 500, 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:

Note: Because the number does not have enough whole digits, we add zeros to its left, up to the rounding position place. The number value is not changing.


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: 0399.66386386386386386...

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: 0399.66386386386386386... ≈ 0 rounded to the nearest thousand (4 whole places).


Or, even simpler.
In any number rounded to whole 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 replace all the digits to the right of it with zeros:

0399.66386386386386386... ≈ 0 rounded to the nearest thousand (4 whole 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. 399.66386 is not halfway between its neighbors.


399.66386 ≈ 0


- 399.66386 ≈ 0


rounded to the nearest thousand (4 whole places)


Number Round Half Down:

Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 399.66386 is not halfway between its neighbors.


399.66386 ≈ 0


- 399.66386 ≈ 0


rounded to the nearest thousand (4 whole 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. 399.66386 is not halfway between its neighbors.


399.66386 ≈ 0


- 399.66386 ≈ 0


rounded to the nearest thousand (4 whole places)


Number Round Half Towards Zero:

Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero. 399.66386 is not halfway between its neighbors.


399.66386 ≈ 0


- 399.66386 ≈ 0


rounded to the nearest thousand (4 whole 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. 399.66386 is not halfway between its neighbors.


399.66386 ≈ 0


- 399.66386 ≈ 0


rounded to the nearest thousand (4 whole 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. 399.66386 is not halfway between its neighbors.


399.66386 ≈ 0


- 399.66386 ≈ 0


rounded to the nearest thousand (4 whole places)


Number Round Ceiling:

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


399.66386 ≈ 1,000


- 399.66386 ≈ 0


rounded to the nearest thousand (4 whole places)


Number Round Floor:

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


399.66386 ≈ 0


- 399.66386 ≈ - 1,000


rounded to the nearest thousand (4 whole places)


More operations like this:

399.66387: Round off the mixed repeating (recurring) decimal number to the nearest thousand (4 whole places)


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 399.66386 to the nearest thousand (4 whole places) May 30 22:49 UTC (GMT)
Round off 1.06798384687983 to the nearest ten (2 whole places) May 30 22:49 UTC (GMT)
Round off 0.2333333337 to the nearest hundredth (2 decimal places) May 30 22:49 UTC (GMT)
Round off 1.06798389367984 to the nearest ten (2 whole places) May 30 22:49 UTC (GMT)
Round off 82.7 to the nearest hundred thousandth (5 decimal places) May 30 22:49 UTC (GMT)
Round off 1.06798386487999 to the nearest ten (2 whole places) May 30 22:49 UTC (GMT)
Round off 0.072587768 to the nearest one (1 whole place) May 30 22:49 UTC (GMT)
Round off 1.06798381556998 to the nearest ten (2 whole places) May 30 22:49 UTC (GMT)
Round off 8,827.6 to the nearest one (1 whole place) May 30 22:48 UTC (GMT)
Round off 7.3075665 to the nearest ten (2 whole places) May 30 22:48 UTC (GMT)
Round off 1.36558 to the nearest one (1 whole place) May 30 22:48 UTC (GMT)
Round off 12.60506 to the nearest hundredth (2 decimal places) May 30 22:48 UTC (GMT)
Round off 1.06798381389389 to the nearest ten (2 whole places) May 30 22:48 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.