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ROUND function

We sat at a round table to make conversation easier. The ancient Egyptian demonstrated that the Earth is round , not flat. Our child's bed has round corners for safety. The baker sold us a round dozen. One hundred is a nice round number. By raising turkeys the farmers were able the more surely to pay their rents. Young girls often acquired a very sufficient dowry, and towns-folk who wished to eat them had to pay round prices for them. The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers.

Numbers do not necessarily match those in definitions. See instructions at Wiktionary: Round Double, MidpointRounding Math. For additional guidance on choosing an overload, see Which method do I call?

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Round Decimal d Rounds a decimal value to the nearest integer, and rounds midpoint values to the nearest even number example. Round Double a Rounds a double-precision floating-point value to the nearest integer, and rounds midpoint values to the nearest even number example. Round Decimal d , Int32 decimals Rounds a decimal value to a specified number of fractional digits, and rounds midpoint values to the nearest even number example. Round Double value , Int32 digits Rounds a double-precision floating-point value to a specified number of fractional digits, and rounds midpoint values to the nearest even number example.

Round Decimal d , MidpointRounding mode Rounds a decimal value to the nearest integer, and uses the specified rounding convention for midpoint values example.

PHP: round - Manual

Round Double value , MidpointRounding mode Rounds a double-precision floating-point value to the nearest integer, and uses the specified rounding convention for midpoint values example. Round Decimal d , Int32 decimals , MidpointRounding mode Rounds a decimal value to a specified number of fractional digits, and uses the specified rounding convention for midpoint values example. Round Double value , Int32 digits , MidpointRounding mode Rounds a double-precision floating-point value to a specified number of fractional digits, and uses the specified rounding convention for midpoint values example.

This is a complete list of parameters for the Round method. For the parameters used by each overload, see the overload syntax above.


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Decimal or Double , depending on the type of the value to be rounded. A numeric value of the same type as d , a , or value , but rounded either to an integer or to the specified number of decimal digits.

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See Midpoint values and rounding conventions for information about rounding numbers with midpoint values. When rounding midpoint values, the rounding algorithm performs an equality test. Because of problems of binary representation and precision in the floating-point format, the value returned by the method can be unexpected.

For more information, see Rounding and precision. If an overload with a Double parameter is called with Double. NaN , the method returns Double. If it is called with Double. NegativeInfinity , the method returns Double. Rounding involves converting a numeric value with a specified precision to the nearest value with less precision.


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For example, you can use the Round Double method to round a value of 3. In a midpoint value, the value after the least significant digit in the result is precisely half way between two numbers. In these cases, the nearest value can't be easily identified without a rounding convention. The Round method supports two rounding conventions for handling midpoint values:. Rounding away from zero Midpoint values are rounded to the next number away from zero.

This form of rounding is represented by the MidpointRounding. Rounding to nearest, or banker's rounding Midpoint values are rounded to the nearest even number. For example, both 3.

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Rounding to nearest is the standard form of rounding used in financial and statistical operations. When used in multiple rounding operations, it reduces the rounding error that is caused by consistently rounding midpoint values in a single direction. In some cases, this rounding error can be significant. The following example illustrates the bias that can result from consistently rounding midpoint values in a single direction. The example computes the true mean of an array of Decimal values, and then computes the mean when the values in the array are rounded by using the two conventions.

In this example, the true mean and the mean that results when rounding to nearest are the same. However, the mean that results when rounding away from zero differs by. By default, the Round method uses the rounding to nearest convention. The following table lists the overloads of the Round method and the rounding convention that each uses. In order to determine whether a rounding operation involves a midpoint value, the Round method multiplies the original value to be rounded by 10 n , where n is the desired number of fractional digits in the return value, and then determines whether the remaining fractional portion of the value is greater than or equal to.

This is a slight variation on a test for equality, and as discussed in the "Testing for Equality" section of the Double reference topic, tests for equality with floating-point values are problematic because of the floating-point format's issues with binary representation and precision. This means that any fractional portion of a number that is slightly less than. The following example illustrates the problem.

Regardless of the rounding convention, However, as the output from the example shows, it does not. The example uses the "R" standard numeric format string to display the floating point value's full precision, and shows that the value to be rounded has lost precision during repeated additions, and its value is actually As the example also shows, this problem does not occur if we simply assign the constant value Problems of precision in rounding midpoint values are most likely to arise in the following conditions:.

In Rb, these syntaxes were added to round to any number of decimal or significant digits and to round duration values:.

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This can cause unexpected results when combined with the round function. For display purposes, use sprintf to control the exact display of a number as a string. This function fully supports tall arrays. For more information, see Tall Arrays. Code generation does not support char or logical data types for X. This function fully supports distributed arrays. Choose a web site to get translated content where available and see local events and offers.

Based on your location, we recommend that you select: Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. All Examples Functions More. Trial Software Product Updates. This is machine translation Translated by. Examples collapse all Round Matrix Elements. Round to Specified Number of Decimal Digits.

Round to Nearest Multiple of Controlling Number Display While Rounding.