# Which number cannot be represented exactly on a digital computer?

A digital computer stores fractions as a finite number of bits $b_1, b_2, b_3, \ldots , b_n$ representing

$\frac{b_1}{2} + \frac{b_2}{2^2} + \cdots + \frac{b_n}{2^n}.$

Which of the following numbers cannot be represented exactly in this manner?

×