FDP Strategy Guide Ch. 2, Problem 3

[KelseyR968]

Here's the question:

Which integer values of b would give the number 2002 / 10 raised to the -b a value between 1 and 100?

The solution given is {-2, -3}. Why wouldn't it be {2, 3}? Isn't the exponent -b the same as (-1)(b), such that a negative value for be would make the exponent positive?

[RonPurewal]

you want the EXPONENT to be positive.

the two solutions that fall within the desired range are:
2002/10^2 = 2002/100 = 20.02
and
2002/10^3 = 2002/1000 = 2.002

so you want the EXPONENT to be either 2 or 3.

this means either
–b = 2
or
–b = 3

so, either b = –2 or b = –3.

[RonPurewal]

if you don't see why the positive values of b FAIL to work ... then just TRY THEM!

i.e., try plugging in b = 2 or b = 3.
if you use either of those values, you'll be dividing by a decimal, and you'll get a HUGE number as the final result.
specifically,
if you plug in b = 2, you'll get 2002/(10^–2) = 200200.
if you plug in b = 3, you'll get 2002/(10^–3) = 2002000.