Data Representation: Number systems

Number type	Description	Example
Natural numbers	A natural number is a whole number used in counting	ℕ = {0,1,2,...}
Integer numbers	An integer number is a whole number either positive or negative	ℤ = {...,-2,-1,0,1,2,...}
Rational numbers	A rational number is any number that can be expressed directly as a fraction	ℚ = {7/1,21/7,1/4,2/9,...}
Real numbers	A real number is any number that can exist in the real world including irrational numbers e.g. π	ℝ = {7,21/7,1/4,√2,π,...}
Ordinal numbers	Ordinal numbers are used for giving the position of objects	e.g. 1st, 2nd, 3rd, ...

Natural numbers tend to be used for counting, while real numbers are used for measurement.

Units of measurment

Historically the terms kilobyte, megabyte, etc have often been used when kibibyte, mebibyte, etc are meant. These are in fact different. One set uses binary prefixes and works in powers of 2 and the other uses decimal prfixes and works in powers of 10.

Binary Prefixes			Decimal Prefixes
Name	Symbol	Number of bytes	Name	Symbol	Number of bytes
kibibyte	KiB	2¹⁰ = 1024	kilobyte	KB	10³ = 1000
mebibyte	MiB	2²⁰ = 1,048,576	megabyte	MB	10⁶ = 1,000,000
gibibyte	GiB	2³⁰ = 1,073,741,824	gigabyte	GB	10⁹ = 1,000,000,000
tebibyte	TiB	2⁴⁰ = 1,099,511,627,776	terabyte	TB	10¹² = 1,000,000,000,000

Knowledge check

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