Calcite | Level 5

## Apparent SAS calculation error

Consider the following code.  a = b and yet SAS determines that a < b.  Why?

data x;
a = 11*10;
b = (11/10)*100;
if a = b then put 'equal';
if a > b then put 'greater';
if a < b then put 'less';
output;
run;

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Accepted Solutions
Super User

## Re: Apparent SAS calculation error

Do a google search for "sas numeric precision", and you will find the answer.

In short: decimal fractions cannot be exactly represented as binary data, so you introduce minimal aberrations during the calculation. When testing for equality, always use the ROUND() function before you compare.

BTW 11/10 can't even be represented exactly as a decimal value, as it resolves to 1.1 periodic.

3 REPLIES 3
Super User

## Re: Apparent SAS calculation error

Do a google search for "sas numeric precision", and you will find the answer.

In short: decimal fractions cannot be exactly represented as binary data, so you introduce minimal aberrations during the calculation. When testing for equality, always use the ROUND() function before you compare.

BTW 11/10 can't even be represented exactly as a decimal value, as it resolves to 1.1 periodic.

Super User

## Re: Apparent SAS calculation error

Computers cannot store numbers exactly.
Almost all software applications can generate such an error.

https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.5&docsetId=lrcon&docsetTarget=p0ji1u...

## Re: Apparent SAS calculation error

Hello @SAS1ns1ghts,

See this 2020 post for a detailed explanation why for SAS (under Windows) 0.07*100>7 (!). Your example, 1.1*100>110, is quite similar. The length of the period in the binary (periodic) fraction representing the decimal fraction 1.1 is 4, not 20 as in the case of 0.07, but the basic pattern is the same: a periodic fraction is rounded internally and the rounding error propagates in calculations.

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