Transcript Rational and Irrational Numbers

Rational and Irrational
Numbers
A rational number is a
number that can be expressed
as a fraction or ratio
(rational). The numerator and
the denominator of the fraction
are both integers.
When the fraction is
divided out, it becomes a
terminating or repeating
decimal.
(The repeating decimal
portion may be one
number or a billion
numbers!) Rational
numbers can be ordered
on a number line.
6 or
-2 or
6
1
2
1
can ALSO be written as
6.0
can ALSO be written as
-2.0
can ALSO be written as
.5
can ALSO be written as
-1.25
2
3
2
3
can ALSO be written as
.66 repeating
can ALSO be written as
0.666666…
21
55
can ALSO be written as
0.38181818…
can ALSO be written as
0.62855421687
1
2
5
4
53
83
where the decimals
repeat after 41 digits
Be careful when using a
calculator to determine if a
decimal number is irrational.
The calculator may not be
displaying enough digits to
show you the repeating
decimals, as was seen in the
last example above.
Hint: When asked to write a rational number
(given in decimal form) as a fraction,
"say" the decimal using place value to
help form the fraction.
2.3456
Examples:
Write each rational
number as a fraction:
1. 0.3 2. 0.007 3. -5.9
• Hint:
• When checking to see which fraction is
larger, change the fractions to decimals by
dividing.
Examples: Which of the given numbers is
greater?
Using full calculator display…..
.6666666667 > .25
-2.333333333 > -3.666666667
• An irrational number
cannot be expressed as
a fraction.
Also, irrational numbers
cannot be represented
as terminating or
repeating decimals.
• Irrational numbers are non-terminating, nonrepeating decimals.
Examples of IRRATIONAL
NUMBERS are:

= 3.141592654
2
= 1.414213562…..
AND 0.12122122212………
Note: Many students think that  is the
terminating decimal, 3.14, but it is
not. Yes, certain math problems ask you
to use  as 3.14, but that problem is
rounding the value of  to make your
calculations easier.  is actually a nonending decimal and is an irrational
number.
Rational and
irrational numbers
are real numbers.