percentages

A percentage is a mathematical concept representing a fraction of 100. It is denoted using the percent sign (%). The term originates from the Latin "per centum," meaning "by the hundred." Percentages are used extensively to express proportions, ratios, and rates in fields like finance, statistics, and everyday situations.

The calculation of a percentage involves identifying a part relative to a whole. The basic formula is: (Part / Whole) × 100%. For example, if 15 students out of a class of 30 pass a test, the percentage who passed is (15 / 30) × 100% = 50%. This signifies that half of the class passed.

Percentages are crucial for comparing different quantities, as they standardize figures to a common base of 100. A change from one value to another is often expressed as a percentage increase or decrease. The formula for percentage change is: ((New Value - Original Value) / Original Value) × 100%. An increase from 50 to 75 is a ((75-50)/50)×100% = 50% increase.

Applications are widespread. In finance, interest rates on loans and savings are given as percentages. In retail, discounts are advertised as a percentage off the original price. Scientific data often reports concentrations or success rates as percentages. Understanding percentages is fundamental to interpreting data, managing personal finances, and making informed comparisons in daily life. They simplify complex ratios into easily understandable figures.