Converting Percent
Converting percent means changing a percent to a decimal or fraction, or changing a decimal or fraction to a percent.
Formula
\text{percent to decimal: divide by 100; decimal to percent: multiply by 100}
Definition
Converting a percent means changing it into a fraction or a decimal: to change a percent to a decimal, divide by $100$ (move the decimal point two places left); to change a decimal to a percent, multiply by $100$ (move it two places right). The full set of rules: percent to decimal ($p\% = p/100$), decimal to percent ($d = d \times 100\%$), fraction to percent ($a/b \times 100\%$), and percent to fraction ($p\% = p/100$, then simplify); repeating decimal percents (like $33.333\ldots\%$) arise from fractions whose denominators have prime factors other than $2$ and $5$. Formally, this conversion is an isomorphism $f: \mathbb{Q} \to \mathbb{Q}$ given by $f(x) = x/100$ with inverse $f^{-1}(x) = 100x$, essential in probability, statistics, and finance whenever probabilities, relative frequencies, or interest rates are expressed as percents.
Example
$45\%$ to decimal is $45/100 = 0.45$; a decimal like $0.72$ to percent is $0.72 \times 100 = 72\%$; and a fraction like $3/4 = 0.75 = 75\%$. Converting $37.5\%$ to a fraction gives $375/1000 = 3/8$, while $5/6 \times 100 = 83.333\ldots\% = 83$ and $1/3\%$ (a repeating percent, since $3$ does not evenly divide $100$). A probability $p = 0.034$ expressed as a percent is $3.4\%$, but arithmetic still needs the decimal form: $P(A \text{ and } B) = p_A \times p_B = 0.034 \times 0.21 = 0.00714 = 0.714\%$, and mixing percent and decimal forms in the same calculation is a common source of error.
Key Insight
Moving the decimal point two places is a handy shortcut, but understanding why helps: percent means "per hundred," so $45\% = 45/100$, and dividing by $100$ shifts the decimal point two places left. Percent-to-fraction conversion sometimes produces a non-terminating decimal in the percent, $1/3 = 33.333\ldots\%$, which does not mean anything is wrong with $1/3$, only that $3$ does not evenly divide $100$. The convention of using percent rather than raw probability has cognitive roots: Gigerenzer's research on statistical literacy shows that natural frequency representations ("$34$ out of $1000$") produce far fewer reasoning errors than equivalent percent or decimal probability statements, a practical argument for percent as a teaching tool.