Answer:
14/45
Step-by-step explanation:
So we have the fraction:
[tex]0.3\bar1=0.31111...[/tex]
We can do this algebraically. Follow to following steps:
Let's let this number equal to n. Thus:
[tex]0.31111...=n[/tex]
Since there is only 1 digit repeating, let's multiply everything by 10. So:
[tex]3.1111...=10n[/tex]
Now, subtract n from both sides:
[tex]3.1111-n=10n-n[/tex]
On the left, substitute the number for n. On the right, combine like terms:
[tex]3.1111...-0.31111...=9n[/tex]
All of the 1s will cancel. So:
[tex]3.1-0.3=9n[/tex]
Subtract:
[tex]2.8=9n[/tex]
Divide both sides by 9:
[tex]n=2.8/9[/tex]
Remove the decimal by multiplying both sides by 10:
[tex]n=28/90[/tex]
Reduce:
[tex]n=14/45[/tex]
And we're done!
Use a calculator to check:
[tex]14/45\stackrel{\checkmark}{=}0.31111...[/tex]
