Rational Numbers
• A rational number is a real number that can be written as a ratio of two integers.
• A rational number written in decimal form is terminating or repeating.
Irrational Numbers
• An irrational number is a number that cannot be written as a ratio of two integers.
• Irrational numbers written as decimals are non-terminating and non-repeating.
What are integers?• Integers are the
whole numbers and their opposites.
• Examples of integers are
6-120186-934
Using Exponents
If “a” is a real number and “n” is a natural number, then an = a•a•a•••a•a (n factors of a).
where n is the exponent, a is the base, and an is an exponential expression. Exponents are also called powers.
To find the value of a whole number exponent:
100 = 1, 20 = 1, 80 = 1, #0 = 1101 = 10, 21 = 2, 81 = 8, #1 = #102 = 10 x 10 = 100, 22 = 2 x 2 = 4, 82 = 8 x 8 = 64103 = 10 x 10 x 10 = 1000, 23 = 2 x 2 x 2 = 8104 = 10 x 10 x 10 x 10 = 10,000 24 = 2 x 2 x 2 x 2 = 16(-10)3 = (-10)(-10)(-10) (12).5 =
Using the Identity Properties “additive identity”
Zero is the only number that can be added to any number to get that number.
0 is called the “identity element for addition” a + 0 = a Example 1: 4 + 0 = 4
“multiplicative identity”
One is the only number that can be multiplied by any number to get that number.
1 is called the “identity element for multiplication”
a • 1 = a Example 2: 4 • 1 = 4
The Real Number SystemThe Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
3
1/2-2
15%2/3
1.456
-0.7
0
√3 2π
−√5 2
3π4
The Real Number The Real Number SystemSystem Real Numbers
Rational Numbers Irrational Numbers
31/2 -2
15%
2/3
1.456
- 0.7
0
√3 2π
−√5 2
3π4
Integers
The Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
31/2
-2
15%
2/3
1.456
- 0.7
0
√3 2π
−√5 2
3π4
Integers Whole
The Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
31/2
-2
15%
2/3
1.456
- 0.7
0√3 2
π−√5 2
3π4
Integers Whole Natural
Finding Additive inversesFinding Additive inverses
For any real number x, the number –x is the For any real number x, the number –x is the
additive inverse of x.additive inverse of x.
Example 1:Example 1:Number
Inverse Additive
6 - 6- 4 4
- 8.7 8.70 0
2
32
3−
Symbol Meaning Example
= is equal to 4 = 4
≠ is not equal to 4 ≠ 5
< is less than 4 < 5
≤ is less than or equal -4 ≤ -3
> is greater than -4 > -5
≥ is greater than or equal -8 ≥ - 10