Question

Express the following rational number into decimal and state the kind of decimal expansion 2/7, 22/3, 327/200

Answer 1

Answer:

$\frac{2}{7}=0.285714285714........$

$\therefore\frac{2}{7}$ has recurring decimal expansion.

$\frac{22}{3}=7.333333333........$

$\therefore\frac{22}{3}$ has recurring decimal expansion.

$\frac{327}{200}=1.635$

$\therefore\frac{327}{200}$ has terminating decimal expansion.

Also any rational number of the form

$\frac{p}{2^m*5^n}$ will have

terminating decimal expansion.

We can write $\frac{327}{200}$ as

$\frac{327}{2^3*5^2}$

so, it will have terminating decimal expansion