Real Numbers, Algebraic Expressions, Exponents, and Scientific Notation – Vocabulary Flashcards

Vocabulary flashcards covering key concepts from real numbers, algebraic expressions, exponents, and scientific notation.

Real numbers

All numbers that can appear on the number line, including both rational and irrational numbers.

Variable

A symbol (often a letter) that represents an unknown value in expressions or equations.

Integer

A whole number that can be positive, negative, or zero (no fractional part).

Rational number

A number that can be written as a ratio of integers (a/b, with b ≠ 0) and has a terminating or repeating decimal.

Irrational number

A number that cannot be written as a ratio of integers; its decimal expansion neither terminates nor repeats.

Absolute value

The distance of a number from zero on the number line; |x| ≥ 0.

PEMDAS

Order of operations: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Distributive property

The rule a(b + c) = ab + ac (and (a + b)c = ac + bc) that distributes multiplication over addition.

Combine like terms

Process of adding or subtracting coefficients of terms that have the same variable part.

Like terms

Terms that have the same variable raised to the same power (e.g., 3x and -5x).

Exponent

A small number written as a superscript that indicates how many times to multiply the base by itself.

Product rule (exponents)

When multiplying like bases: a^m · a^n = a^(m+n).

Power rule

(a^m)^n = a^(m n).

Power of a product

(ab)^n = a^n b^n.

Power of a quotient

(a/b)^n = a^n / b^n (with b ≠ 0).

Quotient rule (same base)

(a^m)/(a^n) = a^(m−n).

Zero exponent

Any nonzero base raised to the 0 power equals 1: a^0 = 1 (a ≠ 0).

Negative exponent

A^(−n) = 1/(A^n) for A ≠ 0.

Scientific notation

Expressing a number as a × 10^n where 1 ≤ |a| < 10 and n is an integer.

Standard notation

The ordinary decimal or integer form of a number.

Conversion between standard and scientific notation

Process of switching between decimal form and scientific notation by moving the decimal point.

Algebraic expression

A combination of constants and variables joined by addition, subtraction, multiplication, and division.

Constant

A fixed value in an expression that does not change.

Monomial

A single term, such as 7x^2 or -4y.

Polynomial

A sum of one or more monomials.

Repeating decimal

A decimal that has a repeating block of digits (a rational number).

Term

A part of a polynomial separated by addition or subtraction; can be a constant, a variable term, or a product of factors.