Decimal
A decimal is a number that uses a decimal point to show values that are parts of a whole, based on powers of ten.
Definition
A decimal is a number that has a dot (the decimal point) in it; digits after the decimal point are parts of a whole, smaller than $1$, and since our number system is based on tens, decimals are just fractions written in base-ten shorthand. Formally, a decimal is a base-ten positional representation of a real number, where each digit after the point represents a power of one-tenth (tenths, hundredths, thousandths, and so on), and decimals are either terminating, repeating, or non-repeating/non-terminating. A decimal expansion is the representation of a real number $x$ as $\sum_{n=-k}^{\infty} a_n \cdot 10^{-n}$ with each $a_n$ in $\{0,1,\ldots,9\}$; for a rational $p/q$ in lowest terms, the decimal terminates iff $q = 2^a \cdot 5^b$, and otherwise repeats, while non-repeating infinite decimals are irrational.
Example
$0.5$ is the same as $1/2$ (five tenths), $0.25$ is the same as $1/4$ (twenty-five hundredths), and $\$3.75$ means $3$ whole dollars and $75$ hundredths of a dollar. More generally, $3.147 = 3 + 1/10 + 4/100 + 7/1000$, while $0.333\ldots = 1/3$ repeats forever and $3.14159\ldots = \pi$ never terminates or repeats (irrational). The decimal $1/7 = 0.142857142857\ldots$ has period $6$, since the repeating block $142857$ is a cyclic number whose multiples are cyclic permutations of itself.
Key Insight
Decimals are fractions in disguise: instead of writing $3/10$, you can write $0.3$, and decimals are easier to add on a calculator and easier to compare, you just line up the decimal points. A decimal is rational if and only if it terminates or repeats, an elegant fact connecting the arithmetic of fractions to the base-ten representation system and providing a practical test for rationality. Formally, the decimal expansion is a group homomorphism from $\mathbb{Q}$ to the additive group of formal power series in $1/10$; its kernel consists of numbers with two decimal representations, like $0.999\ldots = 1.000\ldots$, a non-uniqueness that arises at these dyadic-type edge cases.