|
Question |
Answer |
| 1 |
What is a rational number? |
Can we slightly widen the question to be as follows?
What is a rational number
AND
how do I remember? |
| 2 |
Right, my question is:
What is a rational number
AND
how do I remember? |
Well, a rational number is any number capable of being expressed as a fraction
where the numerator (top number) is any integer ( ... -3 -2 -1 0 1 2 3 ...)
AND
the denominator (bottom number) is any positive integer ( 1 2 3 ...).
Now you may feel that you can remember the above
or you may feel that the following is easier to recall.
| Rational Number |
= |
p |
|
where p is any integer | |
| |
| q | | where q is any positive integer |
Or, either of the following two may be used as a memory aid:
| Rational Number |
= |
Integer | |
|
| Positive Integer |
| Rational Number |
= |
... -3 -2 -1 0 1 2 3 ... | |
|
| 1 2 3 ... |
|
| 3 |
So is a number like 8 a rational number? |
Yes.
8 is capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
|
| 4 |
Is a large number such as 123, 500 a rational number? |
Yes.
123, 500 is capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
|
| 5 |
Is a negative number such as
-21 a rational number? |
Yes.
-21 is capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
|
| 6 |
Is the decimal 0.5 a rational number? |
Yes.
0.5 is capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
|
| 7 |
Is the decimal
2.1
a rational number? |
Yes.
2.1 is capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
|
| 8 |
Is the decimal
-0.25
a rational number? |
Yes.
-0.25 is capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
|
| 8 |
Is zero a rational number? |
Yes.
Zero is capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
| 0 |
= |
0 | |
|
| Any positive integer |
You can divide zero by any positive integer and still have zero.
|
| 9 |
Is the π a rational number? |
No.
π is NOT capable of being expressed as a fraction
where the top is an integer
AND
the bottom is a positive integer.
|
| 10 |
So π is not a rational number
but is there a special name for non-rational numbers? |
Yes.
Irrational numbers.
|
| 11 |
So an irrational number
is a number NOT capable of being expressed as a fraction where the numerator is an integer and the denominator is a positive integer? |
Correct.
Well done.
|