Percentage - Converting Fractions and Decimals to Percentage

Understanding Percentage: The word 'percent' comes from the Latin 'per centum', meaning 'per hundred'. A percentage is a fraction with a denominator of $100$. Visually, imagine a large square divided into a $10$ by $10$ grid of $100$ smaller squares; each small square represents $1\%$.

The Percentage Symbol: We use the symbol $\%$ to denote percentage. For example, $25$ out of $100$ is written as $25\%$. In a visual diagram, if $25$ squares in a $100$-square grid are shaded blue, the shaded portion is $25\%$.

Converting Fractions via Equivalent Fractions: If the denominator of a fraction is a factor of $100$ (like $2, 4, 5, 10, 20, 25, 50$), you can find an equivalent fraction with a denominator of $100$. For example, to convert $\frac{3}{5}$, multiply both top and bottom by $20$ to get $\frac{60}{100}$, which is $60\%$.

General Rule for Fraction to Percentage: To convert any fraction to a percentage, multiply the fraction by $100$ and attach the $\%$ sign. For instance, $\frac{1}{8} \times 100 = 12.5\%$. This represents $12.5$ parts for every $100$ parts.

Converting Decimals to Percentage: To change a decimal to a percentage, multiply the decimal by $100$. This is done by shifting the decimal point two places to the right. For example, $0.45$ becomes $45\%$, and $0.07$ becomes $7\%$.

Mixed Numbers to Percentage: To convert a mixed number like $1 \frac{1}{2}$ to a percentage, first convert it to an improper fraction $\frac{3}{2}$. Then multiply by $100$ to get $150\%$. Visually, this means you have one full $100$-square grid and half of another grid shaded.

Percentages Greater than $100\%$: When a fraction is improper (the numerator is larger than the denominator) or a decimal is greater than $1.0$, the percentage will be greater than $100\%$. For example, $1.25$ is $125\%$, which signifies more than one whole unit.