Question

Write the following rational number in decimal form and also state either it is terminating or non terminating, repeating decimal:
$\frac{229}{400}$.

Answer 1

The given rational number is $\frac{229}{400}$
To make simplification simple and easy, lets make the denominator multiples of $10$.

Consider $\frac{229}{400}$

$=\frac{229}{4\times 100}$

$=\frac{229}{2^2\times {10}^2}$

$=\frac{229\times 5^2}{2^2\times 5^2\times {10}^2}$ [ Multiplying $\frac{5^2}{5^2}$]

$=\frac{5725}{{10}^2\times {10}^2}$

$=\frac{5725}{10000}$
In the denominator, we have four zero's, so we need place the decimal point after $4$ digits from right to left.

$=0.5725$

Hence, the decimal expansion is $0.5725$.

Here, the decimal expansion terminates after finite number of steps.

$\therefore \frac{229}{400}$ has a terminating decimal form.