How to store only 3 digits after the decimal point?

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Faez Alkadi
Faez Alkadi le 21 Sep 2017
Commenté : Faez Alkadi le 21 Sep 2017
I'm working on R2016a and using round function to get red of the extra digits that I don't need on right side of the decimal point, so I did the following :
so I got:
But I want it to be (stored) as:
Is what i'm doing write ?
Thank you so much.

Réponse acceptée

Walter Roberson
Walter Roberson le 21 Sep 2017
Modifié(e) : Walter Roberson le 21 Sep 2017
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.
  3 commentaires
Walter Roberson
Walter Roberson le 21 Sep 2017
No. IEEE 754 Binary Double Precision is able to exactly represent all integers in the range +/- 2^53, but for N digit decimal numbers, only 2^N out of 10^N can be exactly represented. For example, for 3 digits, 0.000, 0.125, 0.250, 0.375, 0.500, 0.625, 0.750, 0.875 -- only 8 exactly representable 3 digit decimals out of 1000.
2.123 is not exactly representable in IEEE 754 Binary Double Precision. The closest exactly representable number is 2.12300000000000022026824808563105762004852294921875
Faez Alkadi
Faez Alkadi le 21 Sep 2017
Thank you !

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James Tursa
James Tursa le 21 Sep 2017
Modifié(e) : James Tursa le 21 Sep 2017
This is just a display difference. The numbers are the same. E.g.,
>> format long
>> x = 2.123456789123456789
x =
>> y = round(x,3)
y =
>> z = 2.123
z =
>> y == z
ans =
>> format short g
>> y
y =
>> z
z =
If you want to display the number to three decimal places, e.g.,
>> fprintf(' %.3f\n',y)
>> fprintf(' %.3f\n',z)
But keep in mind that 2.123 cannot be represented exactly in IEEE double precision format. The nearest IEEE double precision number to 2.123, converted to an exact decimal representation, is
>> num2strexact(2.123)
ans =


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