Question

Let X=7/30×25 be a rational number.Then X has decimal expansion,which terminates:

a) after four places of decimal
b) after three places of decimal
c) after two places of decimal
d)after five places of decimal​
​

Answer 1

Question:-

Let $x = \frac{7}{30 \times 25}$

be a rational number. Then x has decimal expansion,which terminates:

a) after four places of decimal

b) after three places of decimal

c) after two places of decimal

d) after five places of decimal

Solution:-

Method-1 :-

Given,

$x = \frac{7}{30 \times 25}$

$x = \frac{7}{750} = 0.0093333...$

The number terminates after four decimals.

Method-2 :-

Given,

$x = \frac{7}{25 \times 30}$

$= > \frac{7}{2 \times 3 \times {5}^{3} }$

We know that if a number in the form of p/q will terminate if denominator is of the form

${2}^{n} \times {5}^{m}$

$x = \frac{7}{3} \times \frac{1}{2 \times {5}^{3} }$

Since, 7/3 = 2.333...

And we have 2× 5³

The x will terminate after 4 decimals

Final answer:-

Correct answer is (a) after four decimals