Mathematics

Number and Quantity

# Notation and structure of the number system

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Notation and structure of the number system

Notation and Structure of the Number System

Types and Properties of Numbers

- Understand the different types of numbers in the number system, including
**natural numbers**,**integers**,**rational numbers**,**irrational numbers**, and**real numbers**. **Natural numbers**are those used for counting and ordering (e.g., 1, 2, 3).**Integers**include natural numbers, zero, and their negatives (e.g., -2, -1, 0, 1, 2).**Rational numbers**can be written as a fraction where both the numerator and denominator are integers (e.g., 7/3, -4/5). This category also includes integers and natural numbers.**Irrational numbers**cannot be written as a fraction. They do not terminate or repeat, and include numbers like π and √2.- The
**real numbers**are a combination of rational and irrational numbers.

Number Notations

- Get comfortable with
**standard form (or scientific notation)**e.g., 3.4 x 10<sup>5</sup>. - Understand the use of
**surds**to represent the root of a number that cannot be simplified to a rational number (e.g., √2 is a surd). - Know how to convert between
**fractions, decimals, and percentages**and when to use each.

Order of Operations

- Remember the order of operations, often remembered by the acronym
**BIDMAS**, standing for Brackets, Indices, Division, Multiplication, Addition, and Subtraction. - Note that division and multiplication, as well as addition and subtraction, are of equal precedence and should be performed from left to right.

Sequences and Series

- Recognize and work with
**arithmetic sequences**, where each term is a certain number (the common difference) more than the previous term. - Similarly, understand
**geometric sequences**, where each term is a certain number (the common ratio) times the previous term. - Know how to calculate the
**sum of a finite arithmetic series**and the sum of a**finite and infinite geometric series**.

Each of these key points serves as a solid foundation on which to build a deeper understanding of the notation and structure of the number system. Details of the mathematical operations and workings of these number types can then be studied individually for a comprehensive understanding of the subject.