The smallest number in the list $\{0.40,0.25,0.37,0.05,0.81\}$ is
(A) 0.40
(B) 0.25
(C) 0.37
(D) 0.05
(E) 0.81
Solution 1

Since each number in the set is between 0 and 1 , they can be ordered from smallest to largest by comparing their tenths digits first. In order from smallest to largest the list is

$$
\{0.05,0.25,0.37,0.40,0.81\}
$$

The smallest number in the list is 0.05 .

## Solution 2

Consider the equivalent fraction for each decimal:

$0.40=\frac{40}{100}, 0.25=\frac{25}{100}, 0.37=\frac{37}{100}, 0.05=\frac{5}{100}$, and $0.81=\frac{81}{100}$.

Since the denominators all equal 100 , we choose the fraction with the smallest numerator. Therefore, $0.05=\frac{5}{100}$ is the smallest number in the set.