Types of Number © B. Taylor - 2004

N Z Q R Natural Numbers 1, 2, 3, 4, 5, . . . Integers The counting numbers N Natural Numbers 1, 2, 3, 4, 5, . . . Include all the whole numbes and zero Z Integers . . . -3, -2, -1, 0, 1, 2, 3, . . . Include all the integers plus fractions Q Rational Numbers Include all the Rational Numbers plus numbers that cannot be written as fractions R Real Numbers

Factor Prime Number 2, 3, 5, 7, 11, 13, 17, . . . Prime Factor A factor of a number divides exactly into that number Factor eg: Factors of 14 are: 1, 2, 7 and 14 A number with exactly TWO factors: (1 and itself) Prime Number 2, 3, 5, 7, 11, 13, 17, . . . A factor of a number which is also a prime number is called a prime factor Prime Factor

A factor of a number which is also a prime number is called a prime factor

24 = 2 x 2 x 2 x 3 = 2 x 3 24 12 6 3 1 ÷ 2 ÷ 2 ÷ 2 ÷ 3 Prime Factor A factor of a number which is also a prime number is called a prime factor Prime Factor eg 1: Write 24 as a product of Prime Factors 24 12 6 3 1 Keep dividing by prime numbers until you get to an answer of 1 ÷ 2 ÷ 2 ÷ 2 ÷ 3 24 = 2 x 2 x 2 x 3 3 = 2 x 3

REAL NUMBERS Rational Numbers Irrational Numbers These include all the whole numbers and numbers which can be written as a fraction. These are all the and numbers which can NOT be written as a fraction. ALL decimals which recur or terminate can be written as fractions. Examples: pi Square roots of primes and multiples of primes.

Writing a terminating decimal as a fraction (1) Write all the digits after the decimal point (2) Draw a line under these (3) Put a 0 under each digit (4) Put a 1 in front of the 0s (5) Simplify if possible Examples 37 213 013 0.37 0.213 = 0.013 = = 1 00 1 000 1 000 13 = 1000