Question

Can you tell me 6/20 have terminating or non terminating but repeating decimal expansions ,without actual division.(give reasons)

Answer 1

$\huge\tt\underline{Solution:}$

$\dfrac{6}{20}$ = $\dfrac{3}{10}$ _______ (on simplifying)

Since, neither 2 nor 5 is a factor of 3,

°•° $\dfrac{3}{10}$ is in its simplest form.

And, 10 = (2 × 5) = (2^m × 5^n)

Thus, the given number is a terminating decimal.

•°• $\dfrac{3}{10}$ = 0.3

_____________________

To know whether a rational number, such as x, is a terminating or non terminating decimal, let it be in its simplest form, say $\dfrac{p}{q}$

• x is a non terminating decimal if q is not equal to (2^m × 5^n)
• x is a terminating decimal if q = (2^m × 5^n)