Week 2 - Number systems Flashcards
Hindu Arabic numeration system
(types of numbers)
1, 2, 3, 4 = Natural Numbers
0, 1, 2, 3 = Whole numbers
-3, -2, -1, 0, 1, 2, 3 = Integers
1/2 = 0.5, 1/3 = 0.3333 etc. = Rational numbers
Pi, (square root of 2 divided by 1) - Irrational numbers
Prime numbers
Prime numbers are only divisible by the number itself and the number 1
They must only have two different divisors (factors)
2, 3, 5, 7, 11, 13
Composite numbers
Composite numbers have more than two divisors (factors)
The natural numbers (except 1) that are not prime numbers are composite)
4, 6, 8, 9, 10
1 is neither prime or composite
Highest Prime Number
282, 589, 933 - 1
More than 24000 digits
Factors and Multiples
Numbers or algebraic expressions are factors (or divisors) of another number if they multiply to give that number.
Factors of 10 are: 1, 2, 5, 10 (come before the number)
A multiple of a whole number is the product of that number and an integer.
Multiples of 10 are: 10, 20, 30, 40, 50 (come after the number)
Highest Common Factor HCF
The highest or greatest common factor that will
divide two or more other numbers exactly.
E.g.
The factors of 12 are: 1, 2, 3, 4, 6, 12
The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The common factors are: 1, 2, 3, 6
HCF = 6
Lowest Common Multiple LCM
The smallest number that is the multiple of
two or more other numbers.
E.g.
Multiples of 5: 5, 10, 15, 20, 25 (etc)
Multiples of 7: 7, 14, 21, 28, 35 (etc)
Common multiples: 35, 70
LCM = 35
Divisibility
A number that can be divided evenly without leaving a remainder.
Divisible by 2
2 - When the last digit is 0, 2, 4, 6, 8
Divisible by 3
3 - When the sum of digits is divisible by 3.
E.g. Is 2358 divisible by 3?
2 + 3 + 5 + 8 = 18.
18 is divisible by 3, therefore 2358 is divisible by 3
Divisible by 4
4 - When the last 2 digits are divisible by 4
E.g. 1324 = 1000 + 300 + 24
= 4 x 250 + 4 x 25 x 3 + 24
Divisible by 5
Last digit must end in a 5 or 0
Divisible by 6
As 6= 2 x 3, the rules for 2 and 3 must both hold.
E.g. 72
The digits add up to a multiple of 3, and it is an even number
Divisible by 8
Similar to rule 4, but the last 3 digits must be divisible by 8
Divisible by 9
Digits must add up to 9
Hindu Arabic Number System
Expanded notation examples
E.g. Write the following numbers as powers of 10 in expanded notation
Hindu Arabic Number System
Expanded notation examples
E.g. Write the following numbers as powers of 10 in expanded notation
475 = 4 hundreds, 7 tens and 5 ones
= 4 x 100 + 7 x 10 + 5 x 1
= 4 x 10^2 + 7 x 10^1 + 5 x 10^0
Rational vs Irrational Numbers
Rational Numbers: Fractions have a logical and reasonable pattern that repeats (e.g. 0.3333)
Irrational Numbers: Digits continue without pattern, like square and cube root numbers (e.g. Pi: 3.14159)
How many prime numbers are there?
25
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Triangular numbers (diagram with blue dots in triangles)
Natural numbers which can be drawn as dots and arranged in a triangular shape
1, 3, 6, 10
Square numbers (diagram with pink circles in squares)
Natural numbers which can be drawn as dots and arranged in a square shape
E.g. 1, 4, 9, 16
Cubic Numbers
A number raised to the third power which is
indicated by a small 3 to its upper-right.
1 is the first cube number because 1 x 1 x 1 = 1
8 is the second cube number, because 2 x 2 x 2 = 8
27 is the third cube number, because 3 x 3 x 3 = 27
64 is the fourth cube number, because 4 x 4 x 4 = 64
First 4 cube numbers
1, 8, 27, 64
