In some math word problems that have percentages, I have to use something like (1.08) instead of (.08). Why is this needed?

Question

I have been trying to figure out this SAT word problem that requires me to set up a couple numbers, but I still didn't get the right answer because it needed me to use a percentage like (1.08) instead of (.08).I don't understand the reasoning behind this.

Answer 1

You would use the 1.08 percent to calculate an increase of 8 percent. It turns a two step procedure into a one step procedure.

 

1.08Y = Y + .08Y

 

 

Answer 2

When solving a percentage problem such as this, you can approach it 2 ways. If you just want the amount of the tax charged on a purchase (such as state sales tax), you simply multiply the cost times the percentage as a decimal (.08).  If the question asks what the total price charged with tax, then you can work it 2 ways.  You would multiply the purchase times the tax  (as I just stated), but then you have to add the purchase price as well.  This is because we pay for dinner and tax is charged as well.  Dinner is the 1.00 and the tax is the .08,  because we have to pay both purchase and tax, thus the 1.08 times purchase.  The 2nd way is to just do one step of multiplying the purchase times 1.08, resulting in the same final price as the method above.