Thread: how much paper would I need to write out this number?? (applied use of logarithms)

Got this problem to do....... don't know where to start. Need help!

If 9^(9⁹) is multiplied out and typed on a strip of paper, 3 digits per centimeter, about how many kilometers long would the paper be?

A hint says use the common log to determine the number of digits the number has, but I don't understand what that means

The common log is base 10.

Yes I know that, but I forgot to mention one thing, I revised my post so I'm a bit clearer.

If there are digits in , then solve for in .

Remember to round your value of down, because you cannot have part of a digit.

So I'd solve for x and then use a conversion factor to get the length of the paper? Also, where does the 10^(x-1) come from?

Originally Posted by zachd77

So I'd solve for x and then use a conversion factor to get the length of the paper? Also, where does the 10^(x-1) come from?

, (rounding down to the nearest whole number).

Add 1 to both sides, and we get

.

Three digits per centimeter means you will need

Converting from cm to km, the answer is approximately 1232.31 km.

Wow.. thanks again!!