Unexpected floor() function result?

>> (1.2-floor(1.2))*10
ans =
    2.0000
>> floor((1.2-floor(1.2))*10)
ans =
     1

Have I misunderstood how the floor function interacts with other math operations?

[Albert Hsueh]

>> ((1.2-floor(1.2))*10) == 2

ans =

logical 0

[Albert Hsueh]

I'm guessing this is some really small numerical inpercision in the back end. The following results in the expected result

>> round((1.2-floor(1.2))*10)==2

ans =

logical 1

Answer 1

[Adam Danz]

This is round-off error and is caused by limitation to representing floating point decimals.

1.2-floor(1.2)

ans = 0.2000

1.2-floor(1.2) - 0.2000 % Reveal round-off error

ans = -5.5511e-17

Likewise,

(1.2-floor(1.2))*10

ans = 2.0000

(1.2-floor(1.2))*10 - 2.000 % Reveal round-off error

ans = -4.4409e-16

Here's another example,

4/3

ans = 1.3333

4/3-1

ans = 0.3333

(4/3 - 1)*3 

ans = 1.0000

(4/3 - 1)*3 - 1 % Reveal round-off error

ans = -2.2204e-16

See this answer for a list of references to learn more about round-off error and floating point representation. If there's a specific issue you need to solve to avoid the problem, add some details and I may be able to point you in the right direction.