1. What Percent Means: Per Hundred

Percent means per hundred. The symbol \(\%\) is a shortcut for "out of 100."

\[ 37\%=\frac{37}{100}=0.37. \]

Think of percent as a common language. If one class has 18 out of 20 students present and another has 27 out of 30 present, the counts are different. Percents let us compare fairly:
\[ \frac{18}{20}=90\%,\qquad \frac{27}{30}=90\%. \]
Both classes have the same attendance rate.

Three interpretations matter:

• Part of a whole: 25% of a pizza means 25 out of 100 equal parts.
• Rate: 6% sales tax means 6 dollars per 100 dollars.
• Change: 30% increase means the change is 30 out of every 100 of the original amount.

Case study - test score: A student answers 36 questions correctly out of 40. The score is
\[ \frac{36}{40}=0.90=90\%. \]

Common mistake: reading 0.37 as 37%. That is correct. But reading 0.037 as 37% is not; \(0.037=3.7\%\).