542.117144373: Round off the mixed repeating (recurring) decimal number to the nearest ten (2 whole places)

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.

A repeating decimal has a number of decimals that repeat over and over again, infinitely: 542.117144373 ≈ 542.1171443734437344373...

Counting by tens (2 whole places at a time), our number is sitting on the axis of numbers between two consecutive neighboring numbers:
540 < 542.117144373 < 550

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: (540 + 550) ÷ 2 = 545

Our number, 542.117144373 ≈ 542.1171443734437344373..., is smaller than 545, so it is closer to the smaller neighbor: 540

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 4: 542.1171443734437344373...

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 2: 542.1171443734437344373... ≈ 540 rounded to the nearest ten (2 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:

542.1171443734437344373... ≈ 540 rounded to the nearest ten (2 whole places)

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. 542.117144373 is not halfway between its neighbors.

542.117144373 ≈ 540

- 542.117144373 ≈ - 540

rounded to the nearest ten (2 whole places)

Number Round Half Down:

Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 542.117144373 is not halfway between its neighbors.

542.117144373 ≈ 540

- 542.117144373 ≈ - 540

rounded to the nearest ten (2 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. 542.117144373 is not halfway between its neighbors.

542.117144373 ≈ 540

- 542.117144373 ≈ - 540

rounded to the nearest ten (2 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. 542.117144373 is not halfway between its neighbors.

542.117144373 ≈ 540

- 542.117144373 ≈ - 540

rounded to the nearest ten (2 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. 542.117144373 is not halfway between its neighbors.

542.117144373 ≈ 540

- 542.117144373 ≈ - 540

rounded to the nearest ten (2 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. 542.117144373 is not halfway between its neighbors.

542.117144373 ≈ 540

- 542.117144373 ≈ - 540

rounded to the nearest ten (2 whole places)

Number Round Ceiling:

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

542.117144373 ≈ 550

- 542.117144373 ≈ - 540

rounded to the nearest ten (2 whole places)

Number Round Floor:

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

542.117144373 ≈ 540

- 542.117144373 ≈ - 550

rounded to the nearest ten (2 whole places)