Notation and Symbols
You have used many different notations and symbols in your study of
mathematics, including exponential notation and ordering symbols. Here
are some examples for you to review.
A positive integer exponent is used to indicate repeated multiplication of a
For example, the expression 73 is written in exponential notation. It
means 7 Â· 7
Â· 7. The exponent is 3 and the base is 7.
Ordering symbols are used to indicate the relative position of two
numbers on a number line. The number on the left is less than the number
on the right.
For example, -4 is less than 2 because -4 lies to the left of 2.
||Position on Number line
||is equal to
||is not equal to
||is less than
||-4 < 2
||-4 is to the left of 2.
||is greater than
||2 > -4
||2 is to the right of -4.
||is less than or equal to
||-4 ≤ 2
-4 ≤ -4
|-4 is to the left of 2.
||is greater or equal to
||2 ≥ -4
-4 ≥ -4
|- is to the right of -4.
The pointed end of the inequality symbol
always points towards the smaller number.
Thus, â€œfour is less than sevenâ€ is written
4 < 7.
Likewise, â€œseven is greater than fourâ€ is
written 7 > 4.
Which of the following statements are true?
a. -6 > -2
b. -5 < 3
c. 7 ≤ 7
a. False. -6 > -2 is read â€œnegative six is greater than negative two.â€
This statement is false because -6 lies to the left of
-2 on the number
line. Therefore, -6 < -2.
b. True. -5 < 3 is read â€œnegative five is less than three.â€
This is true because -5 lies to the left of 3 on the number line.
c. True. 7 ≤
7 is read â€œseven is less than or equal to 7.â€
This means either â€œ7 is less than 7â€ or â€œ7 is equal to 7.â€ Since 7
= 7, the statement 7
7 is true. (An â€œorâ€ statement is true if either part is
Note: The statement 7 ≥ 7
is also true.