IEEE 754 floating point arithmetic rounding error in c# and javascript

Question

I just read a book about javascript. The author mentioned a floating point arithmetic rounding error in the IEEE 754 standard.

For example adding 0.1 and 0.2 yields

Answer 1

The closest representations of those three numbers in double precision floating point are:

• 0.1 --> 0.10000000000000001 = D(3FB99999 9999999A)
• 0.2 --> 0.20000000000000001 = D(3FC99999 9999999A)
• 0.3 --> 0.29999999999999999 = D(3FD33333 33333333)

The next larger representable number beyond 0.29999999999999999 is:

• 0.30000000000000004 = D(3FD33333 33333334)

The closest representation of

• 0.10000000000000001 + 0.20000000000000001 is 0.30000000000000004

So you are comparing 0.29999999999999999 and 0.30000000000000004. Does this give you more insight as to what is happening?

As far as the use of decimal instead of binary representations, that doesn't work either. Take for example one third:

• 1/3 = 0.3333333333333333333333333333333...

which has no exact representation even using decimal digits. Any computations should always take representation error into account.