Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES
Ms. Graham/Mr. Barlock
Name: _______________________________ Block: _______ Date: _____________
WARM UP
1.
Write down where you were born.
2. Write your name in the circle that best describes that place (be as specific as possible).
Loudoun
Co
VA
Earth
USA
NOTES
In the English language, the words rational and irrational mean:
Rational:
Irrational:
Set Terms:
Term
Definition
A collection of objects
A member of the set
A set containing one or more elements of a parent set. Every
element of a subset is contained in the parent set
Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES
Ms. Graham/Mr. Barlock
Example:
S= {yellow, red, blue, green}
Elements:
A subset of S:
Real Number Subsets:
Subset name:
Set:
Symbol
Natural Numbers
{
}
Whole Numbers
{
}
Integers
{
}
Rational Numbers
{
}
Irrational Numbers
{
}
REAL NUMBERS
Sort the numbers below in to the most specific real number subset:
-4
0
2
1
3
0.09
Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES

2
Example
Natural
Whole
Ms. Graham/Mr. Barlock
1. 8
Integer
0.02345…
25
Rational
Irrational
Real
-4
0
2
1
3
0.09
2

1. 8
25
0.02345…
Rational Numbers:
Definition: A rational number is a number that can be written as a fraction in the form ___,
where a and b are integers and b  ______.
** If a number can be written as a fraction, it is rational. Decimals that do not terminate or do
not repeat cannot be written as fractions, so they are NOT rational. **
Writing integers and mixed numbers as fractions:

Integers can be made into fractions by using the integer as the numerator and _______
as the denominator. Ex: 3 =
Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES

Ms. Graham/Mr. Barlock
Mixed numbers can be converted to ________________ fractions.
Examples – write as fractions:
a) 275
b) -24
c) 5
2
3
d) 1
1
4
Writing Decimals as Fractions:
Three Possibilities:
Decimal _________________
Example: __________
Decimal _________________
Example: __________
Decimal neither ______________ or _______________
Example: __________
Writing terminating decimals as fractions:

Turn the decimal into a fraction: “Read it, write it, reduce it.”
Examples – write the following decimal numbers as fractions:
a) 0.5
b) 0.48
c) 3.25
d) 1.125
Writing repeating decimals as fractions:
Write 0 .8 as a decimal
SHORTCUT METHOD:
1) Let N = the number (decimal): N = 0.888888…
2) Multiply each side by 10
10N = 8.8888888…
3) Subtract N
- N = 0.8888888…
9N = 8
4) Divide
N = ______
1) Pretend the _______ isn’t there; write as a ____________: 0.8 =
2) Subtract 1 from the denominator: 0 .8 =_____
Examples – write each repeating decimal as a fraction:
a) .5
b) 2 .25
c) 5 .6
d) 0 .32
8
10