Question

The distance from the Sun to Mars is an average of 2.1 repeating.

1 times the distance from the Sun to Venus. How can this repeating decimal be expressed as a fraction?

Answer 1

19/9

Explanation:

We are given repeating decimal number 2.1¯.

We know 2.1¯ = 2.1111..... repeating 1's.

Let us assume x is a fraction equals given repating decimal number.

And set it as a first eqaution.

x = 2.1111..... ------------- (equation 1).

Multiplying equation both side by 10 ( because only one digit is repeating after decimal, we multiply by 10).

On multiplying by 10 we get

10*x = 10*2.1111.....

10x = 21.1111...... ----------------- (equation 2)

Subtracting equation 1 from equation 2, we get

10x = 21.1111......

-x = -2.1111.....

_____________

9x = 19.

Now, dividing both sides by 9. we get