round

Round to nearest decimal or integer

Syntax

Y = round(X)

Y = round(X,N)

Y = round(X,N,type)

Y = round(t)

Y = round(t,unit)

Description

Y = round(X) rounds each element of X to the nearest integer. In the case of a tie, where an element has a fractional part of exactly 0.5, the round function rounds away from zero to the integer with larger magnitude.

Y = round(X,N) rounds to N digits:

• N > 0: round to N digits to the right of the decimal point.

• N = 0: round to the nearest integer.

• N < 0: round to N digits to the left of the decimal point.

Y = round(X,N,type) specifies the type of rounding. Specify 'significant' to round to N significant digits (counted from the leftmost digit). In this case, N must be a positive integer.

Y = round(t) rounds each element of the duration array t to the nearest number of seconds.

Y = round(t,unit) rounds each element of t to the nearest number of the specified unit of time.

Examples

Round Matrix Elements

Round the elements of a 2-by-2 matrix to the nearest integer.

X = [2.11 3.5; -3.5 0.78];
Y = round(X)

Y = 2×2

     2     4
    -4     1

Round to Specified Number of Decimal Digits

Round pi to the nearest 3 decimal digits.

Y = round(pi,3)

Y = 3.1420

Round to Nearest Multiple of 100

Round the number 863178137 to the nearest multiple of 100.

round(863178137,-2)

ans = 863178100

Round Elements to Specified Number of Significant Digits

Round the elements of a vector to retain 2 significant digits.

format shortg
x = [1253 1.345 120.44]

x = 1×3

    1.2530    0.0013    0.1204

y = round(x,2,'significant')

y = 1×3

    1.3000    0.0013    0.1200

Controlling Number Display While Rounding

The format command controls how MATLAB® displays numbers at the command line. If a number has extra digits that cannot be displayed in the current format, then MATLAB automatically rounds the number for display purposes. This can lead to unexpected results when combined with the round function.

Consider the result of the following subtraction operation, which displays 5 digits.

format short
x = 112.05 - 110

x = 2.0500

Based on the displayed value of x, rounding x to 1 decimal should return 2.1.

round(x,1)

ans = 2

In fact, the problem here is that MATLAB is rounding x to 5 digits for display purposes. The round function returns the correct answer. Confirm the answer by viewing x with format long, which displays x rounded to 15 digits.

format long
x

x = 
   2.049999999999997

Round Duration Values

Round each value in a duration array to the nearest number of seconds.

t = hours(8) + minutes(29:31) + seconds(1.3:0.5:2.3);
t.Format = 'hh:mm:ss.SS'

t = 1x3 duration
   08:29:01.30   08:30:01.80   08:31:02.30

Y1 = round(t)

Y1 = 1x3 duration
   08:29:01.00   08:30:02.00   08:31:02.00

Round each value in t to the nearest number of hours.

Y2 = round(t,'hours')

Y2 = 1x3 duration
   08:00:00.00   09:00:00.00   09:00:00.00

Input Arguments

X — Input array

scalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array. For complex X, round treats the real and imaginary parts independently.

X must be single or double when you use round with more than one input.

round converts logical and char elements of X into double values.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | char | logical
Complex Number Support: Yes

N — Number of digits

scalar integer

Number of digits, specified as a scalar integer. When you specify N, the round function rounds X to the nearest multiple of 10 ^-N.

If you specify the 'significant' rounding type, then N must be a positive integer.

type — Rounding type

'decimals' (default) | 'significant'

Rounding type, specified as 'decimals' or 'significant'. The rounding type determines whether round considers digits in relation to the decimal point or the overall number of significant digits. N must be a positive integer when you specify 'significant'. In that case, the round function rounds to the nearest number with N significant digits.

The default value is 'decimals', so that round(X,N,'decimals') is equivalent to round(X,N).

Example: round(3132,2,'significant') returns 3100, which is the closest number to 3132 that has 2 significant digits.

Data Types: char | string

t — Input duration

duration array

Input duration, specified as a duration array.

unit — Unit of time

'seconds' (default) | 'minutes' | 'hours' | 'days' | 'years'

Unit of time, specified as 'seconds', 'minutes', 'hours', 'days', or 'years'. A duration of 1 year is equal to exactly 365.2425 24-hour days.

Data Types: char | string

Tips

• format short and format long both display rounded numbers. 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. For example, to display exactly 2 decimal digits of pi (and no trailing zeros), use sprintf('%.2f',pi).

Compatibility Considerations

Rounding to specified number of digits

Behavior changed in R2014b

In R2014b, these syntaxes were added to round to any number of decimal or significant digits and to round duration values:

Y = round(X,N)
Y = round(X,N,type)
Y = round(t)  
Y = round(t,unit)   

Older versions of MATLAB^® support only this syntax, which rounds to the nearest integer:

Y = round(X) 

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Code generation supports only the syntax Y = round(X).

• Code generation does not support char or logical data types for X.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• Code generation supports only the syntax Y = round(X).

• Code generation does not support char or logical data types for X.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

• These syntaxes are not supported:

  Y = round(X,N)

  Y = round(X,N,type)

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).