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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. 19/8please explain i'm having trouble and want to study for a test

Respuesta :

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

[tex]\frac{9x}{9}=19[/tex]

[tex]x=\frac{19}{9}[/tex]

Therefore, 2.1¯ repeating decimal be expressed as a fraction [tex]\frac{19}{9}[/tex].

So, the correct option is option c. 19/9.



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