1. 1-A8 Warm Up 1.
-15 – 6 – [-4 – (-6)]
3. a2 + b – c when a = -6, b = 5, c = -3
Take your test home tonight and get a parent signature.
Return the test by tomorrow to get 2 extra credit points!

2. Algebra 1 Glencoe McGraw-Hill JoAnn Evans
Math 8H
1-8 Number Systems
Algebra Glencoe McGraw-Hill JoAnn Evans

3. What are real numbers?
Real Numbers

4. Natural Numbers
Natural Numbers:
“Counting Numbers”
1, 2, 3, 4, 5, …

5. 0, 1, 2, 3, 4, … Whole Numbers: Natural Numbers and 0 Whole Numbers

6. …-3, -2, -1, 0, 1, 2,… Integers: Positive and Negative Whole Numbers
Natural Numbers
Integers:
Positive and Negative Whole Numbers
…-3, -2, -1, 0, 1, 2,…

7. Rational Numbers can be written as:
When written as decimals they either repeat or terminate.
Rational Numbers
Integers
Whole
Numbers
Natural Numbers

8. Rational Numbers Irrational Numbers
Ex:
These must be represented by a symbol (ex: ),
or as a rounded number, or in radical form because the decimal doesn’t repeat or terminate (stop).
Integers
Whole
Numbers
Natural Numbers

9. Real Numbers Rational and Irrational Numbers are…
Rational Numbers Irrational Numbers
Real Numbers
Integers
Whole
Numbers
Natural Numbers

10. So what isn’t a real number?
When you divide by zero and get no
solution
= i (imaginary numbers)

11. Do you remember the closure property?
A set of numbers is CLOSED under an operation if the result of the operation (the answer) is in the same number set as the two numbers used in the operation.

12. Is the set of whole numbers closed under
Determine whether each set of numbers is closed under the indicated operation:
Is the set of whole numbers closed under
the operation of multiplication?
(When you multiply a
whole number times another whole number,
is the answer always a whole number?)
Remember, the whole numbers are 0, 1, 2, 3, …
Closed

13. Is the set of integers closed under the operation of division?
(When you divide an
integer by another integer,
is the answer always an integer?)
Remember, integers are all positive and negative whole numbers, including 0.
Not closed. A counterexample:

14. Is the set of irrational numbers closed under
the operation of multiplication?
(When you multiply an
irrational number times
another irrational number,
is the answer always an irrational number?)
Remember, irrational numbers are numbers like pi or non-repeating and non-terminating decimals.
Not closed. A counterexample to try on your calculator:

15. Name the set of numbers to which each real number belongs.
Example 1
Example 2
Example 3
Example 4
rational
irrational
natural
rational
whole number
integer
integer
rational

16. Square roots are written with a radical symbol
Square roots are written with a radical symbol The number or expression inside a radical symbol is called the radicand.
radical symbol
radicand

17. A square root is one of two equal factors of a number.
3  3 = 9
The positive square root of 9 is 3.
-3  -3 = 9
The negative square root of 9 is -3.

18. The positive square root of 4 is 2.
The negative square root of 4 is -2.
The positive square root of 225 is 15.
The negative square root of 225 is -15.
Zero has only one square root!
The positive square root of is .
The negative square root of is

20. Some square roots aren’t whole numbers
Some square roots aren’t whole numbers. The square roots of numbers that aren’t perfect squares are IRRATIONAL numbers.
In the case of irrational numbers, approximate the square root by rounding the result to two decimal places and replacing the equal sign with a sign.
Approximate the square roots of:

21. The square root of a negative radicand is undefined!
Negative real numbers do not have square roots because two negative numbers multiplied produce a positive number. =
undefined
The square root of a negative radicand is undefined!
Evaluate each expression: 6 -6
undefined

22. To graph a set of numbers means to draw, or plot, the points named by those numbers on a number line. The number that corresponds to a point on a number line is called the coordinate of that point. • • •

23. Graph – 4, , – 6 and 0 on a number line
Graph – 4, , – 6 and 0 on a number line. Order the numbers from least to greatest. • • • •
is an irrational number. Find its approximation on your calculator, then place it on the number line.
– 6, – 4, 0,