1 The World of Numbers

2 Introducing Numbers! The purpose of this slideshow it to reintroduce you to the world of numbers The purpose of this slideshow it to reintroduce you to the world of numbers Most of these terms should be a “refresher” for you Most of these terms should be a “refresher” for you These terms will be used throughout the grade 9 mathematics course These terms will be used throughout the grade 9 mathematics course

3 Real Numbers (Abbreviated R) Rational Numbers (Abbreviated Q) Irrational Numbers (Abbreviated Q)

4 Real Numbers Real Numbers include all numbers that can be expressed as a decimal! Real Numbers include all numbers that can be expressed as a decimal! A Rational Number is a number that can be written in the fraction form m/n, where m and n are both integers and n cannot be zero A Rational Number is a number that can be written in the fraction form m/n, where m and n are both integers and n cannot be zero An Irrational Number is a number that cannot be written in the fraction form m/n, where m and n are integers and n cannot be zero. An Irrational Number is a number that cannot be written in the fraction form m/n, where m and n are integers and n cannot be zero.

5 Examples of Rational Numbers Rational numbers can be decimals that terminate (written as a fraction, this is 1/8 Rational numbers can be decimals that terminate (written as a fraction, this is 1/8 Rational numbers can be decimals that repeat 0.333…. (written as a fraction, this is 1/3) Rational numbers can be decimals that repeat 0.333…. (written as a fraction, this is 1/3) Rational numbers also include all natural and whole numbers, as well as integers Rational numbers also include all natural and whole numbers, as well as integers

6 Examples of Irrational Numbers Irrational numbers include decimals that do NOT terminate or repeat! For example, … cannot be written as a fraction. Irrational numbers include decimals that do NOT terminate or repeat! For example, … cannot be written as a fraction. If you see a root sign and a prime number underneath (prime numbers are numbers which can only be divided by themselves and 1), then the number is irrational. If you see a root sign and a prime number underneath (prime numbers are numbers which can only be divided by themselves and 1), then the number is irrational.

7 A Closer Look at Rational Numbers Rational numbers include natural numbers, whole numbers, and integers. Rational numbers include natural numbers, whole numbers, and integers. Natural numbers are the set of numbers 1,2,3,4,5,…. Natural numbers are the set of numbers 1,2,3,4,5,…. Whole numbers are the set of numbers, 0,1,2,3,4,5…. Whole numbers are the set of numbers, 0,1,2,3,4,5…. Integers are the set of numbers, Integers are the set of numbers, …-2,-1,0,+1,+2… …-2,-1,0,+1,+2…

8 What Type of Number? 5 is a real number, belonging to the set of rational numbers. It is also a natural number, a whole number, AND an integer! 5 is a real number, belonging to the set of rational numbers. It is also a natural number, a whole number, AND an integer! -2 is a real number, belonging to the set of rational numbers. It is also an integer. -2 is a real number, belonging to the set of rational numbers. It is also an integer is a real number, belonging to the set of rational numbers because it can be written as 1/3. What other type of number is it? is a real number, belonging to the set of rational numbers because it can be written as 1/3. What other type of number is it?

9 Next Steps Now you should be familiar with the difference between a rational and an irrational number. Now you should be familiar with the difference between a rational and an irrational number. You should also be able to classify numbers as natural, whole, and/or integers. You should also be able to classify numbers as natural, whole, and/or integers.

10 ON YOUR OWN! Natural (N) Whole (W) Integer (I) Rational (Q) Irrational (Q) Real (R) … -13