Download I = Rational Numbers

Lesson 6
What is a Rational Number Ch 3.1
(NO CALCULATOR UNIT)
REAL NUMBERS
In mathematics, numbers are classified according to common
characteristics. Every number is classified as belonging to one
or more of the following sets of numbers:
Natural Numbers: N =
Whole Numbers: W =
Integers:
I=
Rational Numbers (Q):
Any number that can be expressed in the form
, where m
and n are Integers and n ≠ 0. The decimal portion of a
rational number terminates or repeats.
:
Irrational Numbers 1. Any number that cannot be expressed in the form
where m and n are Integers and n ≠ 0, is an irrational
number. The decimal portion of an irrational number
neither terminates nor repeats.
2. Suppose x is a positive number that is not the square
of an irrational number. Then the number √ is
irrational.
Real Numbers:
R=
,
Classifying Numbers
REAL NUMBERS:
NUMBERS R
Rational Numbers: Q
0.65
. Integers (I)
-8
8
24
Irrational Numbers:
Numbers Decimals that neither
repeat nor terminate
1.72342563789...
√
√
Rational Or Irrational
1. Which of the following numbers are irrational?
a) √3
b) √16)
d) -√25
e) 0.11111…
c) -1.25
1.25
f) √13
h)
0.6010347…
g) 7
2. Write three rational numbers between each pair of numbers.
a) 2.25 and -3.26
b) -0.35 and -0.36
c) and
Converting Improper Fractions to Mixed Numbers
To change an improper fraction into a mixed number, divide the
numerator by the denominator. The remainder is the numerator of
the fractional part.
Examples:
= 11 ÷ 4
= 13 ÷ 2
=2r3
=6r1
= 2
=6
Converting mixed numbers to improper fractions.
First, you take the mixed number and multiply the denominator by
the whole number. Then add the numerator to that answer. The
denominator just stays the same.
Example:
1
=4x1
= 4+3
=
Lowest Terms If the numerators (top) and the denominator (bottom of a
fraction) can be divided by the SAME number, then it is possible to divide
each of them and reduce the fraction to a smaller one.
Reduce each fraction if possible
a)
b)
c)
!
3. Write the rational number represented by each letter as a
decimal.
4. Write the rational number represented by each letter as a fraction.
5.
Sketch a number line and mark each rational number on it.
Order the numbers from greatest to least.
–2.25, , –1.5, , 0.9
6. Order rational numbers in decimal and/or fraction form.
a) 0.35 , 2.5 , -0.6 , 1.7 , -3.2 , -0.6
7. In each pair, which rational number is greater? Explain how you
know.
a) −7.3, −7.2
b) 1.2, −1.3
(Worksheet 6)