40.3333333338: Round off the (terminating) decimal number to the nearest tenth (1 decimal place)

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.

Our number is sitting on the axis of numbers between two 1 decimal place consecutive neighboring numbers:
40.3 < 40.3333333338 < 40.4

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: (40.3 + 40.4) ÷ 2 = 40.35

Our number, 40.3333333338, is smaller than 40.35, so it is closer to the smaller neighbor: 40.3

Except for 'To Ceiling, To Floor', the rounded off number (both the positive and the negative) will be equal only to this smaller neighbor.

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 3: 40.3333333338

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: 40.3333333338 ≈ 40.3 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:

40.3333333338 ≈ 40.3 rounded to the nearest tenth (1 decimal place)

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. 40.3333333338 is not halfway between its neighbors.

40.3333333338 ≈ 40.3

- 40.3333333338 ≈ - 40.3

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. 40.3333333338 is not halfway between its neighbors.

40.3333333338 ≈ 40.3

- 40.3333333338 ≈ - 40.3

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. 40.3333333338 is not halfway between its neighbors.

40.3333333338 ≈ 40.3

- 40.3333333338 ≈ - 40.3

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. 40.3333333338 is not halfway between its neighbors.

40.3333333338 ≈ 40.3

- 40.3333333338 ≈ - 40.3

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. 40.3333333338 is not halfway between its neighbors.

40.3333333338 ≈ 40.3

- 40.3333333338 ≈ - 40.3

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. 40.3333333338 is not halfway between its neighbors.

40.3333333338 ≈ 40.3

- 40.3333333338 ≈ - 40.3

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.

40.3333333338 ≈ 40.4

- 40.3333333338 ≈ - 40.3

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.

40.3333333338 ≈ 40.3

- 40.3333333338 ≈ - 40.4

rounded to the nearest tenth (1 decimal place)