Question

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Why are these numbers not equal?

The below expression, which evaluates to 0.1, is considered larger than 0.1.

> round(1740/600,0) - 1740/600
[1] 0.1
> (round(1740/600,0) - 1740/600) <= 0.1
[1] FALSE //???!!???
> (round(1740/600,0) - 1740/600) <= 0.1000000000000000000000000000000000000001
[1] TRUE

Thinking that the issue might be due to rounding I tried this with the same result:

> 3 - 2.9
[1] 0.1
> (3 - 2.9) <=0.1
[1] FALSE

So, what gives and how do I fix it without fudging the cutoff?

Answer 1

From the Floating-Point Guide:

Why don’t my numbers, like 0.1 + 0.2 add up to a nice round 0.3, and
instead I get a weird result like 0.30000000000000004?

Because internally, computers use a format (binary floating-point)
that cannot accurately represent a number like 0.1, 0.2 or 0.3 at all.

When the code is compiled or interpreted, your “0.1” is already
rounded to the nearest number in that format, which results in a small
rounding error even before the calculation happens.

What can I do to avoid this problem?

That depends on what kind of calculations you’re doing.

• If you really need your results to add up exactly, especially when
  you work with money: use a special decimal datatype.
• If you just
  don’t want to see all those extra decimal places: simply format your
  result rounded to a fixed number of decimal places when displaying it.
• If you have no decimal datatype available, an alternative is to work
  with integers, e.g. do money calculations entirely in cents. But this
  is more work and has some drawbacks.