$$\frac{405}{99}$$

$$\frac{401}{99}$$

$$\frac{81}{33}$$

$$\frac{802}{198}$$

$$\frac{405}{100}$$

$$3\frac{8}{33}$$

$$3\frac{12}{25}$$

$$3\frac{1}{4}$$

$$3\frac{1}{5}$$

$$\frac{1}{6}$$

$$\frac{1}{3}$$

$$\frac{3}{5}$$

$$\frac{2}{3}$$

$$\frac{21}{10}$$

$$\frac{20}{9}$$

$$\frac{19}{9}$$

$$\frac{19}{8}$$

The decimal number is rational because there is a clear pattern in the decimal digits with the number of 2s before each 7.

The decimal number is irrational because even though the decimal digits follow a​ pattern, the decimal is not a repeating decimal.

The decimal number is irrational because there is no pattern in the digits of the decimal.

The decimal number is rational because it is composed of only 2s and 7s.