Tool to compute roundings, an approximate value of digits/decimal places (rounding down floor, rounding up ceil, rounding to multiple calculator) from a given precision.

Rounding Calculator - dCode

Tag(s) : Data Processing, Arithmetics

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In mathematics, rounding is an approximation of a number to make it simpler or shorter while maintaining an approximate value close to the original.

Rounding is generally represented with a limited decimal expansion (defined by a number of digits after the decimal point) which results in a loss of precision on the value of the number but can make it more practical to use (simplification of calculations) or display it (fewer numbers).

There are several possible rounding calculators, the main ones are rounding to the nearest, rounding by default and rounding by excess.

dCode allows rounding (or approximate value) from an exact value, to the desired number, the rounded default is closest (approximation), i.e. the upper value if the decisive digit is greater than or equal to 5 and the lower value if the decisive digit is less than 5.

Round to ones (no decimal dot), round to tenth (1 one decimal place), round to hundredth (2 two decimal places) or round to thousands (3 three decimal places).

__Example:__ `3.15` is rounded to `3.2` with 1 digit after decimal point (to tenth)

Some textbooks refer to rounding to + infinity for rounding up or - infinity for rounding down, or to 0 for rounding down positive numbers and rounding up negative numbers.

Monetary notations (euros, dollars, etc.) use a 2-digit precision format

dCode calculates the nearest multiple (rounded up/superior or rounded down/inferior to the multiple) according to the formula:

Let $ x $ be the number to round and $ m $ be the desired multiple, then round to the multiple $$ = \left\lfloor \frac{x}{m} + \frac{1}{2} \right\rfloor \times m $$

__Example:__ `123` can be rounded to the closest multiple of 5 so: `125`.

The ceiling rounding (or rounding by excess) is in the upper rounding.

__Example:__ `1.2` is ceil rounded to `2`

Floor rounding (or rounding by default) is the lower rounding.

__Example:__ `1.7` is floor rounded to `1`

Truncation is the removal of digits beyond a certain precision, without taking into account any rounding.

__Example:__ `2.89` truncated to 1 decimal value gives `2.8`

The significant digits are the figures (of a decimal number) known with certainty. They depend on the measuring tool, but also on the rounding done.

__Example:__ `0.0123` has 3 significant digits (`1,2,3`)

All rouding (by default) of 0.99999999… are 1.

Mathematically speaking $ 0.999\dots = 1 $

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Cite as source (bibliography):

*Rounding Calculator* on dCode.fr [online website], retrieved on 2024-06-18,

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https://www.dcode.fr/rounding-calculator

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