Lesson 3
Negative Numbers
Real values of less than nothing
Page 104
You are correct. We reached
b − 1 as the result of our division rule
(b2)/(b3) = b(2 − 3) = b − 1
and we cab see by writing out
b2 and
b3 fully that
(b2)/(b3) = (b × b)/(b × b × b) = (1)/(b)
so we can define
b − 1 as equal to
(1)/(b).
By similar reasoning , we can define any negative exponent
b − n = (1)/(bn).
In words:
b − n means 1 divided by
bn. For example:
2 − 1 = (1)/(21) = (1)/(2);
2 − 2 = (1)/(22) = (1)/(2 × 2) = (1)/(4);
2 − 3 = (1)/(23) = (1)/(2 × 2 × 2) = (1)/(8).
We can now, using this new definition, write both proper fractions and whole numbers as powers of a particular base.
How would you write (1)/(3) as a power of 3, using this new definition?
Answer to Self-Test Question 9, Lesson 3 :
