Express $0.\overline{5}$ as a common fraction in lowest terms.

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Explanation:

means that the 5's go on forever because of that horizontal bar over top. So we can write it as

The three dots indicate it goes on forever following that pattern.

Let

x = 0.55555....

Multiply both sides by 10 to move the decimal point 1 spot to the right

10x = 5.55555....

Notice how both x and 10x involve a decimal number such that we have a string of 5's going on forever. If we subtract the two equations, then 10x-x becomes 9x, while the (5.55555....) - (0.55555....) simplifies to 5. The decimal portions cancel out when we subtract since they line up perfectly. We're effectively subtracting 5-0 when we cross off the decimal portions.

After those subtractions, we're left with 9x = 5 which solves to x = 5/9 when you divide both sides by 9.

Use of a calculator should show that 5/9 = 0.555555.... to help confirm the answer. Your calculator may show the last digit to be a 6 instead of a 5, but this is due to rounding. Ideally you should have a string of infinitely many 5's, but the calculator can only how so many digits.

sinn is the total amount of students now and m were the students before, you subtract them both (n-m) and divide that by m. then, since to get a percentage from a fraction you have to multiply by 100, your answer should look like this: n-m/m*100

step-by-step explanation: