Question

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

How can this repeating decimal be expressed as a fraction?

A. 21/10
B. 20/9
C. 19/9
D. 19/8

Please explain i'm having trouble and want to study for a test

Answer 1

The correct option will be: C.
`(19)/(9)`

Step-by-step 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= (19)/(9)`

So, the given repeating decimal be expressed in a fraction as
`(19)/(9)`