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Types of Numbers

LachlanMcDermott1Suivre

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- 1 MrGregoryOnline.com Mr. McDermott Fractions & Decimals 31/8
- 2 MrGregoryOnline.com Recap: Yesterday we looked at two types of decimals: Recurring & Terminating Look back at the definitions in your workbooks if you can’t remember the difference! These types of decimals represent a set of numbers called RATIONAL numbers. There is also a 3rd type of decimal: Non- Terminating which represent a very special set of numbers we call IRRATIONAL This will be our focus for today :)
- 3 MrGregoryOnline.com Warm Up: Make the target number Use all four sets of numbers to find the target 100 2 75 3 1 10 356 75 3 1 8 25 2 100 3 6 8 50 4 100 1 6 7 50 4 1. You can add, subtract, multiply and divide. 2. You can use as many or as little of the numbers as you want. 3. Each number can only be used once.
- Types of numbers Please take some notes in your workbooks as the definitions for each of these number classifications appear (include a couple of examples for each as well) Natural numbers – Real numbers - Integers - Rational numbers - Irrational numbers - Square numbers - Cube numbers - Prime numbers -
- Types of numbers
- 6 MrGregoryOnline.com LI: WALT Investigate the concept of irrational numbers, including π SC 3 SC 2 SC 1 Terms Learn the special names given to different types of numbers. Calculate Calculate and identify square and cube numbers. Advanced Identify prime numbers.
- 7 MrGregoryOnline.com Learn the special names given to different types of numbers. Real Integer Rational Natural These are the counting numbers Includes all the whole numbers and zero Includes all the numbers you currently know A number that can be expressed as a ratio of two integers (Recurring or Terminating) There are five number types (apart from whole numbers) that we need to know at this level. 0 Irrational Irrational numbers cannot be expressed as a ratio of two integers. (Always Non- Terminating) Natural Numbers 0, 1, 2, 3, 4, … Real Numbers 3, 1 .62, -3.75, 4 5 , 𝜋 Integer s …, -4, -3, -2, -1, 0, 1, 2, … Rational Numbers 7 , 3.65, 0.0024, -0.24, 0.333333… Irrational Numbers 2 , 𝜋, 5 0 , 𝑒
- 8 MrGregoryOnline.com Where do the numbers go? B e f o r e c l i c k i n g , s e e i f y g u e s s w h i c h c a t e g o r y e a c h n u m b e r b e l o n g s i n . 2 𝜋 −7 1 2 − 5 23 −1 0.45 3 What does this mean? 2 𝑎𝑛𝑑 𝜋 are real and irrational − 5 23 , 1 2 𝑎𝑛𝑑 0.45 are real and rational −7 𝑎𝑛𝑑 − 1 are real, rational and integers 3 is real, rational, an integer and a natural number
- 9 MrGregoryOnline.com Quiz – Question 1 Which of these sets of numbers contains no rational numbers? 12, 1 5 , −15 A C D B −3.401, 99, 0.2345 … −8, − 169, 3 2 5 225, 0, 0.45 The … means that the numbers continue, therefore this number is not rational Attempt to answer all quiz questions in your book before clicking to reveal answer
- 10 MrGregoryOnline.com Quiz – Question 2 What is the best classification for - 6? A C D B Irrational number, real number Integer, rational number, real number Whole number, integer, real number Rational number, real number
- 11 MrGregoryOnline.com Quiz – Question 3 Which of the following square roots is an irrational number? A C D B − 18 81 12 1 169 Because, the root of 12 is 3.46410… A, B and C have rational answers.
- 12 MrGregoryOnline.com Quiz – Question 4 Given the following numbers, identify the irrational numbers. A C D B 34 5 3.64 0 E −3.444 F 5 9 G −4 H 2𝜋
- 13 MrGregoryOnline.com Quiz – Question 5 The number 0.7 belongs to which of these sets? Name all that apply. A C D B Natural Whole Rational E Irrational F Integer Real
- 14 MrGregoryOnline.com Calculate and identify square and cube numbers. What are they? How do we calculate them? When a number is multiplied by itself you get a square number The name "square number" comes from the fact that these particular numbers of objects can be arranged to fill a perfect square. The symbol for squared is ². So, 3 squared can be written as 32 12 = 1 × 1 = 1 22 = 2 × 2 = 4 52 = 5 × 5 = 25 This means that 1, 4 and 25 are square numbers. Can you think of any more?
- 15 MrGregoryOnline.com Calculate and identify square and cube numbers. What are they? How do we calculate them? A cube number is a number multiplied by itself 3 times The name “cube number" comes from the fact that these particular numbers of objects can be arranged to fill a perfect cube. The symbol for cubed is 3. So, 3 cubed can be written as 33 13 = 1 × 1 × 1 = 1 33 = 3 × 3 × 3 = 27 This means that 1 and 27 are cube numbers. Can you think of any more?
- 16 MrGregoryOnline.com Quiz – Question 1 What is 52? 10 A C D B 125 25 50
- 17 MrGregoryOnline.com Quiz – Question 2 What is 43? 16 A C D B 64 12 512
- 18 MrGregoryOnline.com Quiz – Question 3 Which of these numbers are square numbers? 9 A C D B 36 18 86 E 110 F 81 G 256 H 75
- 19 MrGregoryOnline.com Quiz – Question 4 Which of these numbers are cube numbers? 100 A C D B 144 125 27 E 343 F 81 G 2150 H 8000
- 20 MrGregoryOnline.com Quiz – Question 5 Which of these numbers are neither square or cube numbers? 169 A C D B 85 729 196 E 156 F 1 G 8 H 4913
- 21 MrGregoryOnline.com Identify prime numbers. What are they? How do we find them? A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. I.e. it can only be divided by 1 and itself without leaving a remainder. Is the number 25 a prime number? Is there any number that divides into 25 without leaving a remainder? 25 ÷ 5 = 5 No, 25 cannot be a prime number.
- 22 MrGregoryOnline.com Identify prime numbers. What are they? How do we find them? A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. I.e. it can only be divided by 1 and itself without leaving a remainder. Is the number 9 a prime number? Is there any number that divides into 9 without leaving a remainder? 9 ÷ 3 = 3 No, 9 cannot be a prime number.
- 23 MrGregoryOnline.com Identify prime numbers. What are they? How do we find them? A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. I.e. it can only be divided by 1 and itself without leaving a remainder. Is the number 7 a prime number? Is there any number that divides into 7 without leaving a remainder? 𝐼 𝑐𝑎𝑛′ 𝑡 𝑡ℎ𝑖𝑛𝑘 𝑜𝑓 𝑎𝑛𝑦 Yes, 7 must be a prime number.
- 24 MrGregoryOnline.com Sieve of Eratosthenes 276 BC 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Eratosthenes was a Greek born in Cyrene in modern-day Libya. As a mathematician, poet, athlete, geographer, astronomer, and music theorist. He invented the Sieve of Eratosthenes, an algorithm for finding prime numbers still used today. He sketched the course of the Nile River and correctly predicted its source. He also may have accurately calculated the distance from the Earth to the Sun and calculated the circumference of the Earth with stunning accuracy and Steps: 1. Shade in 1 because 1 is not a prime. 2. Leave 2 and shade in all multiples of 2. (2, 4, 6, 8, 10, ...) 3. Leave 3 and shade in all multiples of 3. ... 4. Leave 5 and shade in all multiples of 5. ... 5. Continue this process until finished. Prime numbers to 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.
- 25 MrGregoryOnline.com Test Your Knowled Before clicking see if you can Identify which numbers go where. (Numbers can go in more than one place) Platinum 15 – 18 correct Gold Silver Bronze Natural Numbers Integer s Prime Numbers Square Numbers Cube Numbers Rational Numbers −6 7 144 216 −0.32 5 9 5 −6 −6 7 does not go with any of these as it is irrational. −0.32 −0.32 144 144 144 144 216 216 216 216 5 9 5 5 5 5 10 – 14 correct 5 – 9 correct 1 – 4 correct
- 26 MrGregoryOnline.com Early Finishers Be mindful of those around you but feel free to watch this awesome video which demonstrates my personal favourite irrational number: The Golden Ratio also known as the divine proportion. https://www.youtube.com/watch?v =sj8Sg8qnjOg

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