Question

211/125,Is the number have terminating decimal expansion and why?

Answer 1

Hello,

Answer: Yes,the number have terminating decimal expansion

Solution:

As we know that, rational numbers are those which can be represented in the form of p/q,where q ≠ 0.

The rational numbers those having denominator in the form of
${2}^{n} \times {5}^{m}$
are of terminating decimal expansion. where n,m are positive integers ,can be zero too.

and those don't have denominator in the above said form,are non terminating repeating decimal.

$\frac{211}{125} \\ \\ = \frac{211}{ {5}^{3} } \\ \\ or \: \\ = \frac{211}{ {5}^{3} \times {2}^{0} }$
This the number is terminating decimal.
$\frac{211 \times {2}^{3} }{ {5}^{3} \times {2}^{3} } \\ \\ = \frac{1688}{1000} \\ \\ = 1.688$
hope it helps you

Answer 2

Hi ,

******************************************
Let x = p/q be a rational number ,

such that the prime factorisation of

' q ' is of the form 2^n5^m , where

n and m are non - negative integers.

Then , x has a decimal expansion

which terminates .

*********************************************

Here ,

x = 211/125 = p/q

q = 125 = 5³

q is of the form 2^n5^m , where

n = 0 , m = 3 ,

Therefore ,

211/125 is a terminating decimal.

I hope this helps you.
: )