Number Systems in Mathematics

These flashcards cover key vocabulary and concepts related to number systems in mathematics, which include natural numbers, whole numbers, integers, rational and irrational numbers, and operations with these numbers.

Natural Numbers

The set of counting numbers starting from 1, 2, 3, … without any upper limit.

Whole Numbers

Natural numbers including zero (0, 1, 2, 3, …). There is no greatest whole number.

Integers

The set of whole numbers and their negative counterparts (…, -3, -2, -1, 0, 1, 2, 3, …).

Rational Numbers

Numbers that can be expressed in the form p/q, where p and q are integers and q ≠ 0.

Irrational Numbers

Numbers that cannot be expressed as a fraction of two integers; their decimal representation is non-terminating and non-repeating.

Real Numbers

The set of all rational and irrational numbers.

Terminating Decimal

A decimal that has a finite number of digits after the decimal point.

Non-terminating Repeating Decimal

A decimal that continues indefinitely but has a repeating pattern.

Number Line

A straight line that represents numbers as points and helps in visualizing their order.

Fundamental Operations

The basic arithmetic operations which include addition, subtraction, multiplication, and division.

Standard Form of a Rational Number

A rational number expressed in the form p/q where p and q are integers and q > 0, with no common factors other than 1.

Equivalent Rational Numbers

Rational numbers that represent the same value, even if they have different numerators and denominators.

Rounding Off Numbers

Adjusting a number to a specified degree of accuracy by increasing or decreasing it.

Finding Rational Numbers Between Two Numbers

The process of identifying any number of rational numbers that lie between two distinct rational numbers.