1.4: Round off the pure repeating (recurring) decimal number to the nearest ten thousandth (4 decimal places)

1.4 rounded to the nearest ten thousandth (4 decimal 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.

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.

A repeating decimal has a number of decimals that repeat over and over again, infinitely: 1.4 ≈ 1.444444444444444...

Our number is sitting on the axis of numbers between two 4 decimal place consecutive neighboring numbers: 1.4444 < 1.4 < 1.4445

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: (1.4444 + 1.4445) ÷ 2 = 1.44445

Our number, 1.4 ≈ 1.444444444444444..., is smaller than 1.44445, so it is closer to the smaller neighbor: 1.4444

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 4: 1.444444444444444...

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 4: 1.444444444444444... ≈ 1.4444 rounded to the nearest ten thousandth (4 decimal places).

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:

1.444444444444444... ≈ 1.4444 rounded to the nearest ten thousandth (4 decimal 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. 1.4 is not halfway between its neighbors.

1.4 ≈ 1.4444

- 1.4 ≈ - 1.4444

rounded to the nearest ten thousandth (4 decimal places)

Number Round Half Down:

Numbers that are halfway between two neighbors are rounded off to the smaller neighbor. 1.4 is not halfway between its neighbors.

1.4 ≈ 1.4444

- 1.4 ≈ - 1.4444

rounded to the nearest ten thousandth (4 decimal 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. 1.4 is not halfway between its neighbors.

1.4 ≈ 1.4444

- 1.4 ≈ - 1.4444

rounded to the nearest ten thousandth (4 decimal places)

Number Round Half Towards Zero:

Numbers that are halfway between two neighbors are rounded off to the neighbor which is closer towards zero. 1.4 is not halfway between its neighbors.

1.4 ≈ 1.4444

- 1.4 ≈ - 1.4444

rounded to the nearest ten thousandth (4 decimal 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. 1.4 is not halfway between its neighbors.

1.4 ≈ 1.4444

- 1.4 ≈ - 1.4444

rounded to the nearest ten thousandth (4 decimal 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. 1.4 is not halfway between its neighbors.

1.4 ≈ 1.4444

- 1.4 ≈ - 1.4444

rounded to the nearest ten thousandth (4 decimal places)

Number Round Ceiling:

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

1.4 ≈ 1.4445

- 1.4 ≈ - 1.4444

rounded to the nearest ten thousandth (4 decimal places)

Number Round Floor:

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

1.4 ≈ 1.4444

- 1.4 ≈ - 1.4445

rounded to the nearest ten thousandth (4 decimal 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