Percents as Fractions

$80\mathrm{\%}$ means 80 per hundred, so $80\mathrm{\%}=\frac{80}{100}$. The greatest common factor of 80 and 100 is 20, so divide the top and the bottom by 20. $$\frac{80}{100}=\frac{80÷20}{100÷20}=\frac{4}{5}$$ So the answer is $\boxed{{\displaystyle 4\mathrm{/}5}}$. Reducing does not shrink the amount, it just names the same slice of storage with smaller numbers.

A percent is a number of hundredths, so $250\mathrm{\%}=\frac{250}{100}$. The greatest common factor of $250$ and $100$ is $50$, so divide the top and the bottom by $50$. $$\frac{250}{100}=\frac{250÷50}{100÷50}=\frac{5}{2}$$ So $250\mathrm{\%}$ in lowest terms is $\boxed{{\displaystyle 5\mathrm{/}2}}$. Going past $100$ is fine, it just means more than one whole, and $\frac{5}{2}$ is $2.5$, the two and a half times the bakery sold.

$-45\mathrm{\%}$ means $-45$ out of $100$, so $-45\mathrm{\%}=\frac{-45}{100}$. Both $45$ and $100$ are divisible by $5$, and dividing gives $\frac{-45÷5}{100÷5}=\frac{-9}{20}$. Since $9$ and $20$ share no factor bigger than $1$, that is lowest terms, so $\boxed{{\displaystyle -9\mathrm{/}20}}$. The minus sign rides along on the numerator and changes nothing about how you reduce.

$38\mathrm{\%}={\displaystyle \frac{38}{100}}=38÷100$, and dividing by $100$ moves the decimal point two places to the left. Start at $38.$, hop the point left once to get $3.8$, then left again to land at $0.38$. So $38\mathrm{\%}=\boxed{{\displaystyle 0.38}}$.

A percent is a count out of one hundred, so $0.4\mathrm{\%}$ means $\frac{0.4}{100}$. Dividing by $100$ slides the decimal point two places to the left. Starting at $0.4$, one slide gives $0.04$ and a second slide gives $0.004$, with zeros filling the empty places. So $0.4\mathrm{\%}=\boxed{{\displaystyle 0.004}}$.

A decimal becomes a percent when you multiply it by $100$, and multiplying by $100$ just slides the decimal point two places to the right. Start with $0.41$. Slide the point past the $4$ to get $4.1$, then past the $1$ to get $41$. So $0.41\times 100=41$, which means $0.41=41\mathrm{\%}$. The answer is $\boxed{{\displaystyle 41}}$.

To make a decimal into a percent, multiply by $100$, which slides the decimal point two places to the right. From $0.073$, one slide gives $0.73$ and a second gives $7.3$, so $0.073=7.3\mathrm{\%}$ and the number you type is $\boxed{{\displaystyle 7.3}}$. There were three digits after the point, so only two of them clear it and the last one stays behind in the tenths place. That is why the percent is itself a decimal.

Rewrite $\frac{3}{4}$ as an equal fraction whose denominator is $100$. Since $4\times 25=100$, multiply the top and bottom by the same $25$. $$\frac{3}{4}=\frac{3\times 25}{4\times 25}=\frac{75}{100}\mathrm{.}$$ A fraction over $100$ is read directly as a percent, so $\frac{75}{100}=75\mathrm{\%}$. The percent is $\boxed{{\displaystyle 75}}$.

Since $5\times 20=100$, rewrite $\frac{8}{5}$ with a denominator of $100$ by multiplying the top and bottom by $20$. $$\frac{8}{5}=\frac{8\times 20}{5\times 20}=\frac{160}{100}$$ A fraction over $100$ reads straight off as a percent, so the answer is $\boxed{{\displaystyle 160}}$. Because $\frac{8}{5}$ is bigger than one whole, the percent lands above $100$, exactly as expected.

A fraction becomes a percent when you multiply it by $100$. $$\frac{9}{8}\times 100=\frac{9\times 100}{8}=\frac{900}{8}$$ Divide the top and bottom by $4$ to get $\frac{225}{2}$, and $225÷2=112.5$. So the number is $\boxed{{\displaystyle 112.5}}$. It clears $100$ because $\frac{9}{8}$ is more than one whole, and it carries a $\mathrm{.}5$ because halving an odd number leaves a half.

Put both shares in decimal form. Room A is $65\mathrm{\%}$, and dividing by $100$ slides the point two places left, so $65\mathrm{\%}=0.65$. Room B is $\frac{3}{5}$, and $3÷5=0.60$, which you can check with $\frac{3}{5}=\frac{6}{10}=0.60$. Since $0.65>0.60$, Room A has the larger share, option $\boxed{{\displaystyle 1}}$. Values in different forms cannot be judged by eye, so convert them to one shared form first.

Percent means per hundred, so $12.5\mathrm{\%}=\frac{12.5}{100}$. Multiply the top and bottom by $10$ to clear the decimal. $$\frac{12.5}{100}=\frac{12.5\times 10}{100\times 10}=\frac{125}{1000}$$ Both $125$ and $1,000$ share the factor $125$, and dividing each by it gives $\boxed{{\displaystyle 1\mathrm{/}8}}$. Twelve and a half percent being exactly one eighth makes sense, since $\frac{1}{8}$ of a hundred is $12.5$.

Percent means "per hundred," so $55\mathrm{\%}$ is $55$ out of $100$. $$55\mathrm{\%}=\frac{55}{100}$$ Now reduce. The numerator and denominator both share a factor of $5$, so divide each by $5$. $$\frac{55}{100}=\frac{55÷5}{100÷5}=\frac{11}{20}$$ Since $11$ is prime and does not divide $20$, the fraction is in lowest terms. $\boxed{{\displaystyle 11\mathrm{/}20}}$

The word percent means per hundred, so $24\mathrm{\%}$ is $24$ out of $100$. $$24\mathrm{\%}=\frac{24}{100}$$ Now simplify. The greatest factor shared by $24$ and $100$ is $4$, so divide both the numerator and the denominator by $4$. $$\frac{24}{100}=\frac{24÷4}{100÷4}=\frac{6}{25}$$ Since $6$ and $25$ share no common factor larger than $1$, this is fully reduced. $\boxed{{\displaystyle 6\mathrm{/}25}}$

Percent means per hundred, so $320\mathrm{\%}=\frac{320}{100}$. The greatest common factor of $320$ and $100$ is $20$, so divide both parts by it. That gives $\frac{320÷20}{100÷20}=\frac{16}{5}$. Since $16$ and $5$ share no factor bigger than $1$, this is lowest terms, and it is more than one whole because $16>5$. $\boxed{{\displaystyle 16\mathrm{/}5}}$

Percent means per hundred, so the number sits over $100$ and keeps its sign. That gives $-8\mathrm{\%}=\frac{-8}{100}$. The top and bottom share a common factor of $4$, so divide both by $4$. The numerator becomes $-8÷4=-2$ and the denominator becomes $100÷4=25$. Since $2$ and $25$ have no common factor left, the fraction is in lowest terms. So $-8\mathrm{\%}$ equals $\boxed{{\displaystyle -2\mathrm{/}25}}$.

A percent is just a number of hundredths, so $73\mathrm{\%}$ means $\frac{73}{100}$. Dividing by $100$ slides the decimal point two places to the left, turning $73.$ into $0.73$. So the decimal form is $\boxed{{\displaystyle 0.73}}$.

To write a percent as a decimal you divide by $100$, which slides the point two places to the left. Begin with $108$, really $108.0$, and move the point two places left to land between the $1$ and the first $0$. So $108\mathrm{\%}=\frac{108}{100}=\boxed{{\displaystyle 1.08}}$. The result is more than $1$ because $108\mathrm{\%}$ is more than a whole.

A percent is just a number over 100, so $0.6\mathrm{\%}$ means $\frac{0.6}{100}$. Dividing by 100 slides the decimal point two places to the left. Starting from $0.6$, one place left gives $0.06$, and a second place gives $0.006$, with placeholder zeros filling the gaps. So $0.6\mathrm{\%}$ as a decimal is $\boxed{{\displaystyle 0.006}}$.

To turn a decimal into a percent, multiply by $100$, which slides the point two places to the right. So $0.47\times 100=47$, and the number to post is $\boxed{{\displaystyle 47}}$. It also reads straight off, since $0.47=\frac{47}{100}$ is already $47$ per hundred.

To go from a decimal to a percent, multiply by $100$, which slides the decimal point two places to the right. $$0.025\times 100=2.5$$ Sliding the point from $0.025$ two places to the right lands between the $2$ and the $5$, so the value is $2.5\mathrm{\%}$. The number alone is $\boxed{{\displaystyle 2.5}}$.

Multiplying $20$ by $5$ gives $100$, so multiply the top by $5$ as well to keep the same value. $$\frac{7}{20}=\frac{7\times 5}{20\times 5}=\frac{35}{100}$$ A fraction over $100$ reads straight off as a percent, so the number is $\boxed{{\displaystyle 35}}$. Rescaling like this works whenever the denominator divides $100$ evenly.

To turn a fraction into a percent, multiply it by $100$. $$\frac{5}{8}\times 100=\frac{500}{8}=62.5$$ So $\frac{5}{8}$ of the bottle is $62.5\mathrm{\%}$ fruit, and the number is $\boxed{{\displaystyle 62.5}}$.

To write a fraction as a percent, multiply it by $100$. That gives $\frac{11}{5}\times 100=\frac{1,100}{5}$, and $1,100÷5=220$, so $\frac{11}{5}=220\mathrm{\%}$ and the number is $\boxed{{\displaystyle 220}}$. That checks out, since $\frac{11}{5}$ is a bit more than $2$ and $220\mathrm{\%}$ is a bit more than $200\mathrm{\%}$.

Percent means per hundred, so $87.5\mathrm{\%}=\frac{87.5}{100}$. Multiply the top and bottom by $10$ to clear the decimal, which gives $\frac{875}{1000}$. Now reduce. Both numbers are divisible by $125$, and $875÷125=7$ while $1,000÷125=8$, so the fraction becomes $\frac{7}{8}$. Since $7$ is prime and does not divide $8$, this is lowest terms. $\boxed{{\displaystyle 7\mathrm{/}8}}$

Put both into percent form so they can be compared head to head. For the fraction, scale $\frac{9}{20}$ to a denominator of $100$ by multiplying top and bottom by $5$, which gives $\frac{45}{100}=45\mathrm{\%}$. Now line them up, $45\mathrm{\%}$ against $44\mathrm{\%}$. Since $45\mathrm{\%}>44\mathrm{\%}$, option 1 is the larger value. $\boxed{{\displaystyle 1}}$