Question

The distance from the Sun to Mars is an average of 2.1¯ times the distance from the Sun to Venus.

Answer 1

The correct option will be:  C. $\frac{19}{9}$

Explanation

The repeating decimal given is:  $2\bar{.1}$ which means 2.1111111111..........

Suppose, the given number 2.1111111111.......... as $x$

Here the repeating digit is 1 . First, we need to move the decimal point after the repeating digit. So we can do that by multiplying both sides by 10. Thus....

$x= 2.1111111111.........\\ \\ 10x= 21.1111111111.........$

Now subtracting the above two equations , we will get.....

$10x-x= (21.1111111111.........)-(2.1111111111.........)\\ \\ 9x= 19\\ \\ x= \frac{19}{9}$

So, the given repeating decimal be expressed in a fraction as $\frac{19}{9}$