Numerical errors of basic multiple

When using matlab multiple calculation, some errors happen

a = 7*13e-6;
b = 6*13e-6;

the answer is

a = 9.09999999999999999e-5
b = 7.80000000000000000e-5

erroe happened at a but not at b;

So how this error happen and how * works? On what condition the error happen?

[KALYAN ACHARJYA]

Error?

>> a =13e-6
a =
     1.300000000000000e-05
>> 7*a
ans =
     9.099999999999999e-05

[yifwang]

7*13e-6 should be exactly

9.100000000000000e-5

but not

9.099999999999999e-5

error

Answer 1

[Ted Shultz]

These are floating point calculations. Not every number can be represented, and this rounding error can compound when you do math with these imperfect numbers.

"Floating-point error arises because real numbers cannot, in general, be accurately represented in a fixed space."

https://en.wikipedia.org/wiki/Floating_point_error_mitigation

[Ted Shultz]

Here is a thread, with links to other threads that address this in more detail:

https://www.mathworks.com/matlabcentral/answers/41536-why-is-2-24-10-22-4-not-equal-to-0