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

109.5 rounded to the nearest one (1 whole 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.

What does it mean to round off a number?

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.

Counting by units (1 whole place at a time), our number is sitting on the axis of numbers between two consecutive neighboring numbers:
109 < 109.5 < 110


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: (109 + 110) ÷ 2 = 109.5


Our number, 109.5, is equal to the middle of the interval, so it is equally close to the either neighbor. The number will be rounded either to 109 or to 110, depending on the type of rounding below.


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 9: 109.5


If the digit to the right of the 'rounding digit' is equal to 5 and it is the last non-zero digit to the right, then the number will be rounded either to the smaller or to the larger neighbor, depending on the type of rounding.

The digit is 5: 109.5 ≈ 109 or 109.5 ≈ 110 rounded to the nearest one (1 whole place).


Or, even simpler.
In any number rounded to whole places, if the digit to the right of the 'rounding digit' is 5 and it is the last non-zero digit to the right, then either increase the 'rounding digit' by 1 or leave it unchanged, but don't forget to replace all the digits to the right of it with zeros:

109.5 ≈ 110 or 109.5 ≈ 109 rounded to the nearest one (1 whole 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. 109.5 is halfway between its neighbors.


109.5 ≈ 110


- 109.5 ≈ - 109


rounded to the nearest one (1 whole place)


Number Round Half Down:

Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 109.5 is halfway between its neighbors.


109.5 ≈ 109


- 109.5 ≈ - 110


rounded to the nearest one (1 whole 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. 109.5 is halfway between its neighbors.


109.5 ≈ 110


- 109.5 ≈ - 110


rounded to the nearest one (1 whole place)


Number Round Half Towards Zero:

Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero. 109.5 is halfway between its neighbors.


109.5 ≈ 109


- 109.5 ≈ - 109


rounded to the nearest one (1 whole 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. 109.5 is halfway between its neighbors.


109.5 ≈ 110


- 109.5 ≈ - 110


rounded to the nearest one (1 whole 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. 109.5 is halfway between its neighbors.


109.5 ≈ 109


- 109.5 ≈ - 109


rounded to the nearest one (1 whole place)


Number Round Ceiling:

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


109.5 ≈ 110


- 109.5 ≈ - 109


rounded to the nearest one (1 whole place)


Number Round Floor:

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


109.5 ≈ 109


- 109.5 ≈ - 110


rounded to the nearest one (1 whole place)


More operations like this:

Round off the number 109.6. Round off the (terminating) decimal number to the nearest one (1 whole 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

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