Question

The decimal expansion of number 441/ 2^2 * 5^3 * 7 is terminating or non terminating. Is it rational or irrational?

Answer 1

terminating because it can be expressed in form of 2n5m.
rational number

Answer 2

Solution :
______________________________________________________________
Given :
To find the that the number $\frac{441}{2^2 5^3 7}$ is rational & has terminating decimal expansion or not,.

_____________________________________________________________
We know that,.
A rational number is in the form $\frac{p}{q}$(q≠0),.
The fraction $\frac{441}{2^25^37}$ is in the form $\frac{p}{q}$(q≠0 As, 2²×5³×7 ≠ 0),.
Hence, it is rational number,.
_______________________
We know that,
A number with terminal decimal expansions have the denominator  in the form,
$2^m 5^n$ where m & n ∈ W,.
The number $\frac{441}{2^25^37} = \frac{3^27^2}{2^25^37} = \frac{3^27}{2^25^3} = \frac{63}{2^25^3}$
Which the denominator is in the form,
$2^m5^n = 2^25^3$ with m = 2 , n = 3,.
Hence, it has terminal decimal expansion,.
_____________________________________________________________
                                                   Hope it Helps,.