Calcite | Level 5

## 0.4 < 0.4 is True?

Hey everyone. I have this code, which creates two variables one, two, which both are equal to 0.4, but for some reason one = 0.4 but one < 0.4 is true. Can somebody explain this?

data test;
one = 1.9/4.75;
two = 4/10;

if one < two then test = 1;
run;

1 ACCEPTED SOLUTION

Accepted Solutions
Meteorite | Level 14

## Re: 0.4 < 0.4 is True?

The error comes because SAS numbers are represented internally as base 2 floating-point numbers. The numbers which cannot be represented exactly in base 2 in your program are 1.9 and 0.4, both of which are approximate when stored in SAS as numbers.

So one approximate number is calculated as approximately 1.9, divided by 19, and multiplied by 4 (4.75 is represented exactly as 19*2^-2), whereas the other approximate number is calculated by dividing 4 by 10.

This is the reason why you sometimes have problems doing accounting in SAS - once in a while you get some rounding errors, which do not matter at all in scientific calculations or in reporting, but in accounting it means that something is wrong somewhere. Databases and languages more suited for accounting and transactions have a fixed decimal type, which does not have these problems. An in most object-oriented languages you can find classes for rational numbers, which may also work correctly in this case (provided that 1.9 is understood/entered as 19/10, and not a base 2 floating-point approximation).

4 REPLIES 4
Diamond | Level 26

## Re: 0.4 < 0.4 is True?

This is roundoff error, as computers cannot represent certain fractions exactly. You can use the ROUND() function or the FUZZ() function in this case.

``if fuzz(one-two)^=0 then test=1;``
--
Paige Miller
SAS Super FREQ

## Re: 0.4 < 0.4 is True?

I recommend you review the documentation and search for Numeric Precision

Onyx | Level 15

## Re: 0.4 < 0.4 is True?

Agree with @AMSAS suggestion.

As an additional exercise check out this:

```1    data test;
2          one = 1.9/4.75;
3          two = 4/10;
4
5          if one < two then test = 1;
6
7          put (one two) (= binary64. /);
8    run;

one=0011111111011001100110011001100110011001100110011001100110011001
two=0011111111011001100110011001100110011001100110011001100110011010
NOTE: The data set WORK.TEST has 1 observations and 3 variables.
NOTE: DATA statement used (Total process time):
real time           0.00 seconds
cpu time            0.00 seconds
```

Bart

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Meteorite | Level 14

## Re: 0.4 < 0.4 is True?

The error comes because SAS numbers are represented internally as base 2 floating-point numbers. The numbers which cannot be represented exactly in base 2 in your program are 1.9 and 0.4, both of which are approximate when stored in SAS as numbers.

So one approximate number is calculated as approximately 1.9, divided by 19, and multiplied by 4 (4.75 is represented exactly as 19*2^-2), whereas the other approximate number is calculated by dividing 4 by 10.

This is the reason why you sometimes have problems doing accounting in SAS - once in a while you get some rounding errors, which do not matter at all in scientific calculations or in reporting, but in accounting it means that something is wrong somewhere. Databases and languages more suited for accounting and transactions have a fixed decimal type, which does not have these problems. An in most object-oriented languages you can find classes for rational numbers, which may also work correctly in this case (provided that 1.9 is understood/entered as 19/10, and not a base 2 floating-point approximation).

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