Question

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

Answer 1

Answer:

14/45

Step-by-step explanation:

So we have the fraction:

$0.3\bar1=0.31111...$

We can do this algebraically. Follow to following steps:

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

$0.31111...=n$

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

$3.1111...=10n$

Now, subtract n from both sides:

$3.1111-n=10n-n$

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

$3.1111...-0.31111...=9n$

All of the 1s will cancel. So:

$3.1-0.3=9n$

Subtract:

$2.8=9n$

Divide both sides by 9:

$n=2.8/9$

Remove the decimal by multiplying both sides by 10:

$n=28/90$

Reduce:

$n=14/45$

And we're done!

Use a calculator to check:

$14/45\stackrel{\checkmark}{=}0.31111...$