Percent: Practice

A percent is a count out of $100$, so the symbol $\%$ means "divide by $100$."

$25\% = 25 \div 100 = \frac{25}{100}$

That is why you can always replace a percent sign with division by $100$.

A percent is a number over $100$, so drop the percent sign and write the number above $100$.

$37\% = \frac{37}{100}$

To turn a percent into a decimal, divide by $100$, which moves the decimal point two places to the left.

$9\% = 9 \div 100 = 0.09$

Moving only one place would give $0.9$, which is ten times too big.

To turn a decimal into a percent, multiply by $100$, moving the point two places to the right, then attach the percent sign.

$0.5 \times 100 = 50 \;\Rightarrow\; 0.5 = 50\%$

$10\% = 0.1$, so multiply, which just moves the decimal point one place left.

$0.1 \times 70 = 7$

Rewrite the fraction with a denominator of $100$ by scaling top and bottom by $25$.

$\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100} = 25\%$

Multiply by $100$, moving the decimal point two places to the right, and attach the percent sign.

$0.42 \times 100 = 42 \;\Rightarrow\; 0.42 = 42\%$

Divide by $100$, moving the decimal point two places to the left.

$80\% = 80 \div 100 = 0.8$

The trailing zero in $0.80$ can be dropped, so it is $0.8$.

$25\% = 0.25$, which is one quarter, so take a quarter of $40$.

$0.25 \times 40 = 10$

$100\%$ is the whole amount, because $100\% = 1$.

$1 \times 63 = 63$

So $100\%$ of any number is the number itself.

Rewrite the fraction with a denominator of $100$ by scaling top and bottom by $25$.

$\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 75\%$

Divide by $100$, moving the decimal point two places to the left.

$5\% = 5 \div 100 = 0.05$

A single-digit percent needs a leading zero in the tenths place, giving $0.05$.