Understanding floating point representation errors; what's wrong with my thinking?

Question

I\'m having some trouble understanding why some figures can\'t be represented with floating point number.

As we know, a normal float would have sign bit, exponent,

Answer 1

You're thinking about 1* 10^-1, which works for a decimal floating number representation, such as decimal in C#. The normal floating point (such as float, double) uses binary representation, i.e. in powers of 2

Normally, binary is used because they can be more efficiently arranged in bits. Decimal is normally used when absolute decimal precision is required, for example when counting money.