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Rational Numbers
A Rational Number can be made by dividing
two integers.
(An integer is a number with no fractional part.)
Example:
1.5 is a rational number because 1.5 =
3/2 (3 and 2 are both integers)
3
2
1.5 =
Ratio
Rational
Most numbers we use in everyday life are
Rational Numbers.
Here are some more examples:
Number
As a Fraction
Rational
Numbers
5
5/1
Rational Numbers
1.75
7/4
Rational
Yes
Yes
.001
1/1000
Yes
−0.1
−1/10
Yes
0.111...
1/9
Yes
√2
(square root of 2)
?
NO !
Oops! The square root of 2 cannot be written as
a simple fraction! And there are many more such
numbers, and because they are not rational
they are called Irrational .
Another famous irrational number is Pi (π) :
π = 3.14159... =
?
(No Ratio)
?
Irrational
Formal Definition of Rational
Number
More formally we say:
A rational number is a number that can be
in the form p/q
where p and q are integers and q is not
equal to zero.
So, a rational number can be:
p
q
Where q is not zero
Examples:
p
q
p/q
=
1
1
1/1
1
1
2
1/2
0.5
55
100
55/100
0.55
1
1000
1/1000
0.001
253
10
253/10
25.3
7
0
7/0
No! "q" can't be
zero!
Just remember: q can't be zero
Using Rational Numbers
If a rational number is still in the
form "p/q" it can be a little difficult
to use, so I have a special page on
how to:
Add, Subtract, Multiply and Divide
Rational Numbers
Fun Facts ....
The ancient greek mathematician
Pythagoras believed that all
numbers were rational, but one of his
students Hippasus proved (using
geometry, it is thought) that you
could not write the square root of 2
as a fraction, and so it was irrational.
But followers of Pythagoras could not
accept the existence of irrational
numbers, and it is said that Hippasus
was drowned at sea as a punishment
from the gods!
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Irrational Numbers
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