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NAME:__________________________________ Number Sets We group numbers into different categories. We will talk about several different ones and how they are related. 1. The Natural numbers (also known as the ___________________ numbers) Thinks of these like counting on your hand. They are 1, 2, 3, 4, 5, 6, 7 …......and so on. How many natural numbers are there? ______________________ 2. The Whole numbers The same as the Natural numbers but it includes _______________. 3. The Integers These are the same as the Whole numbers but it ALSO includes ________________________. So …...-4, -3 , -2, -1, 0, 1, 2, 3, 4............ 4. The Rational numbers These are any positive or negative numbers that can be written as a _________________. Numbers that can be written as a fraction include: The Natural numbers and integers. For example we can write 3 as ________ and 5 as _______ and -7 as __________ Zero because 0 can be written as a fraction as _____________ Any decimal that ends (does not repeat). For example we can write these as fractions: 0.12 = _____________ 1.2 = _________________ 0.012 = ________________ Any decimal that goes on forever AND repeats. If the decimal REPEATS, we can find a fraction for it. Some examples are: 0.33 = _________ .1212 = _____________ .111 = ______________ 5. The Irrational numbers Any number that CANNOT be written as a _______________. These are ONLY decimal that __________________________ AND __________________________. If a decimal goes on forever with no pattern, we notate it with dots (…) after a while. Examples of Irrational numbers: 3.240294........ π = 3.14159..... 2.34323........ 6. The Real Numbers The Real numbers are the _______________ and ___________________ numbers combined. The Real numbers are ALL of the numbers we will use this year in one combined set. Examples: ___________ __________________ ______________ Relationship between number system diagram: _______________ With your partners, try and figure out which number sets these numbers belong to. Remember, numbers can belong to MORE THAN ONE number set! Find them all! a) 15:____________________ b) 23.5:________________________ c) π :____________________ d) 15/17:____________________________ e) -7:____________________ f) 3.123 :____________________________ HOMEWORK g) 6.145242435..... :_________________ h) 2.546161 :_______________________ I) -10,000 :______________________ j) 42 :____________________________ Name a Real number between 1 and 1.0001:_______________________________ Name an irrational number between 1 and 1.2:_________________________________ Can you think of an example where you add two irrational numbers and get a rational number? Give it below: Can you add two Natural numbers together and get an integer? Give an example: What about adding two Fractions (rational numbers) and getting a Natural Number? Give an example: