MATLAB: Why am I getting .99999999999

format longnumber representation

I'm wondering why numbers are being represented with unusual representations. For example in format long

>> 8.2

ans =

   8.199999999999999

Similarly, >> 13.46

ans =

13.460000000000001

But not all numbers do this.

>> 6.3

ans =

   6.300000000000000

Best Answer

It is ‘floating-point approximation error’. It is similar to the problem of representing the fraction ‘1/3’ in decimal notation: 0.3333....

For a much more extensive discussion, see: Why is 0.3 - 0.2 - 0.1 (or similar) not equal to zero? (link)

Related Solutions

MATLAB: How to store only 3 digits after the decimal point

MATLAB uses IEEE 754 Binary Double Precision to represent floating point numbers. All floating point scheme that use binary mantissas cannot exactly represent 1/10, just like finite decimal representation schemes cannot exactly represent 1/3 or 1/7 .

IEEE 754 also defined a Decimal Double Precision representation scheme, which can represent 2.123 exactly. However, computing those values in software is much slower. The only systems I know of that implement IEEE 754 Decimal Double Precision in hardware are the IBM z90 series.

If you need a certain specific number of decimal places to be stored, then use rationals with a power-of-10 denominator.

MATLAB: Strange approximation during vector creation!

That’s normal. It has to do with floating-point calculations and approximations. See: Why is 0.3 - 0.2 - 0.1 (or similar) not equal to zero? (link) for details.

The only work-around I can imagine is to round them:

V1 = 0:0.2:10;
V2 = round(V1,1);
Test = V1-V2;

The more recent versions of round allow rounding to a specific number of decimal places. If you don’t have it, this anonymous funciton will do the same thing (with the same accuracy):

roundn = @(x,n) round(x .* 10.^n)./10.^n;   % Round ‘x’ To ‘n’ Digits, Emulates Latest ‘round’ Function

Best Answer

Related Solutions

MATLAB: How to store only 3 digits after the decimal point

MATLAB: Strange approximation during vector creation!

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