Convert the following repeating decimal to a fraction in simplest form .31 with the 1 repeating

14/45

Step-by-step explanation:

So we have the fraction:

We can do this algebraically. Follow to following steps:

Let's let this number equal to n. Thus:

Since there is only 1 digit repeating, let's multiply everything by 10. So:

Now, subtract n from both sides:

On the left, substitute the number for n. On the right, combine like terms:

All of the 1s will cancel. So:

Subtract:

Divide both sides by 9:

Remove the decimal by multiplying both sides by 10:

Reduce:

And we're done!

Use a calculator to check:

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)