Comparing Quantities - Converting Fractions and Decimals to Percentages

The term 'Percent' is derived from the Latin phrase 'per centum', meaning 'per hundred', and is represented by the symbol $\%$. You can visualize this using a $10 \\times 10$ grid containing $100$ small equal squares; shading $25$ of these squares represents $25\%$.

To convert a fraction into a percentage, multiply the fraction by $100$ and append the $\%$ sign. For example, converting $\\frac{1}{2}$ involves calculating $(\\frac{1}{2} \\times 100)\% = 50\%$. Visually, this indicates that half of the total area of a shape is shaded.

To convert a decimal to a percentage, multiply the decimal value by $100$. This is equivalent to shifting the decimal point two places to the right. For instance, $0.75$ becomes $75\%$. In a visual model like a progress bar, this would be represented by $75$ out of $100$ equal segments.

A percentage can be converted into a fraction by placing the numerical value over $100$ and removing the $\%$ symbol, then simplifying the fraction. For example, $40\% = \\frac{40}{100} = \\frac{2}{5}$. This represents taking $2$ parts out of every $5$ available.

To convert a percentage to a decimal, divide the number by $100$. This is visually represented by moving the decimal point two places to the left. Thus, $8.5\%$ becomes the decimal $0.085$.

When dividing a whole into different percentage parts, the sum of all parts must always equal $100\%$. For example, if a pie chart is divided into two sections where one is $35\%$, the other section must represent $100\% - 35\% = 65\%$.

Percentages can exceed $100\%$, indicating that the quantity is greater than the original whole. This can be visualized as having more than one full $100$-square grid. For example, $150\%$ represents $1.5$ times the original quantity.