About Numbers
Mathematics grows by connecting definitions, patterns, models, calculations, and proof. This page builds the topic from basic ideas toward applications and deeper reasoning.
Place Value
A digit changes value with position.
Learn MoreZero
Zero represents no quantity and acts as a placeholder.
Learn MoreNegative Numbers
Negative values extend the number line below zero.
Learn MoreFractions
Fractions represent ratios or parts.
Learn MoreDecimals
Decimals are fractions built on powers of ten.
Learn MoreIrrational Numbers
Some numbers cannot be written as ratios of integers.
Learn MoreExponents
Exponents describe repeated multiplication.
Learn MoreNumber Systems
Humans have invented many numeral systems.
Learn MorePlace Value
Base ten uses positions worth powers of ten, and decimals extend the same idea to tenths, hundredths, and beyond.
Zero
Zero made positional notation far more powerful and is the additive identity because adding it changes nothing.
Negative Numbers
They describe debt, temperatures below zero, positions below a reference point, and motion in opposite directions.
Fractions
A numerator counts parts and a denominator defines their size, while equivalent fractions can represent the same value.
Decimals
They are especially useful for money, measurement, data, and calculators.
Irrational Numbers
Pi and the square root of two have nonterminating, nonrepeating decimal expansions.
Exponents
They compactly express very large or very small quantities and are essential in algebra and science.
Number Systems
Tally marks, Roman numerals, abaci, and Hindu-Arabic place value show different ways to record number.