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
( b 2 )/( b 3 ) b ( 2 − 3) b − 1
and we cab see by writing out
b 2 and
b 3 fully that
( b 2 )/( b 3 ) ( 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 )/( b n )
In words:
b − n means 1 divided by
b n . 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 )
Answer to Self-Test Question 9, Lesson 3 :
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