You have exactly $120 to spend on a new outfit. if your state has 8% sales tax, what is the highest pre-tax price you can pay without going over budget?

From the information given, the maximum that can be spent has to be enough to buy the outfit and cater for the sales tax as well and not exceed 120 dollars.

so we have the following logic:

outfit price + tax = 120 dollars

let us get the value of the tax first, so:

8% of 120  = ?

8/100 * 120 = ?

0.08 *120 =  

The tax 9.60 dollars.

We now subtract this tax from the total amount to be spent, so:

120 - 9.60 = 110. 40

Therefore the highest pre-tax price to be paid  without going over budget is has to be 110 dollars and 40 cents.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents