Question

Please help. Need help

Answer 1

Answer:

C

Step-by-step explanation:

To do this, let's let the decimal equal n. Thus:

$2.\bar1=n$

There is only one digit repeating, so let's multiply both sides of the equation by 10:

$21.\bar1=10n$

Now, subtract n from both sides:

$21.\bar1-n=10n-n$

On the right, it becomes 9n. However, the left, however, expand, the decimal. In other words:

$21.1111...-2.1111...=9n$

All of the repeating 1s will cancel out. Thus:

$21-2=9n$

Subtract:

$19=9n$

Divide both sides by 9:

$n=\frac{19}{9}$

And since we set the decimal equal to n originally...

$2.\bar1=\frac{19}{9}$

And we're done!

Notes:

This is the algebraic way to write a repeating decimal into a fraction. You can, of course, always just use a calculator and guess and check.

Answer 2

It's A. 21/10

What I did to get this. Is i wrote down 2.1 as a fraction: 2.1/1 then multiplied 10 to both the numerator and the denominator. (2.1 x 10)/(1 x 10)=21/10.

I hope this helps. I'm not sure if the "repeating" matters that much to the point of a different answer...