Question

After how many digits will decimal 27/ 5^4. 2^3. 3^2 terminate

Answer 1

Answer:

The number terminates after

4 decimal places.

Explanation:

27/(5⁴×2³×3²)

= (27)/(5⁴×2³×9)

= 3/(5⁴×2³)

= (3×2)/(5⁴×2⁴)

= 6/(5×2)⁴

= 6/(10)⁴

= 6/10000

= 0.0006

Therefore,

After 4 decimal places the

given number terminates.

••••

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$

$\bf\huge{\implies\dfrac{27}{25^4 \times 2^3\times 3^2}}$  

$\bf\huge{\implies\dfrac{27}{25^4 \times 2^3\times 9}}$  

$\bf\huge{\implies\dfrac{3}{5^4 \times 2^3}}$  

$\bf\huge{\implies\dfrac{3\times 2}{5^4 \times 2^4}}$  

$\bf\huge{\implies\dfrac{6}{(5\times 2)^4}}$  

$\bf\huge{\implies\dfrac{6}{(10)^4}}$  

$\bf\huge{\implies\dfrac{6}{10000}}$  

= 0.0006

Hence

$\bf\huge\bf\huge{\boxed{\bigstar{{ Terminates\: after\: 4\: decimal\: places}}}}$