There is not much that can be done to figure out how to write .15 as a fraction, except to literally use what the decimal portion of your number, the .15, means. Since there are 2 digits in 15, the very last digit is the 100th decimal place. So we can just say that .15 is the same as 15/100.
To change a percent to a decimal we divide by 100. This is the same as moving the decimal point two places to the left. For example, 15% is equivalent to the decimal 0.15. Notice that dividing by 100 moves the decimal point two places to the left.