Luttrell 2012
7
Name: ______________________
Date: _____
1b – Number Systems
Complex Numbers
- All numbers are complex. Their form is
a + bi
. These numbers will be taught later!
Real Numbers
– numbers found on the “number line”. If written as a complex number, they would look like
a+0i.
Imaginary numbers
- points not on the standard number line. If written as complex, they would have form 0+b
i
.
Zero
- It is both real and imaginary.
Rational Numbers
– Real numbers that can be expressed as a ratio of two integers. If written as a decimal, they
would be terminating or repeating.
Irrational Numbers
- reals that CANNOT be expressed as a ratio of integers. If written as a decimal, they would
be nonterminating and nonrepeating decimals.
Transcendental Numbers
- irrational numbers that can NOT be solved by algebraic methods
Integers
- whole numbers and their opposites
Non-integers
- another name for a reduced fraction where 1 is NOT in the denominator.
Whole numbers
- 0, 1, 2, 3…
Natural Numbers (counting numbers)
- 1, 2, 3…
Digits
- whole numbers from 0 to 9, those numbers which make up our numerals
Even
- integers divisible by 2
Odd
- integers that are NOT divisible by 2
Positive
- reals greater than 0
Negative
- reals less than 0
Answer the following about numbers:
1. On a separate piece of paper, create a hierarchy for the number systems above.
For each branch, list three examples of the number system.
2. Which of the following is not a rational number?
3.1
3.01
3.111...
3.1234322344523...
3½
3. Which of the following is not a rational number?
3.4
-3.4
3.444...
-3.444
3.040040004...
4. Which is not an integer? 2 -2 0 ½
4
2
5. What type of number is this: (rational, irrational, integer, real...)
A. -3.4
B.
5
C.
12
D. 0
6. Explain which decimals are rational numbers? How can you tell them from an irrational number?