The number in scientific notation is in the form [tex] m\cdot10^n [/tex] where [tex] n [/tex] is an integer and [tex] m [/tex] is any real number written as decimal. But in normalized notation, [tex] m [/tex] is greater than or equal 1 and less than 10.
So, if the number is between 0 and 1, in order to wirte it in scientific notation we have to move the decimal point to the right, as many times as needed to get a number from the interval [tex] [1,9) [/tex]. But by doing so, it's like we're multiplying the number by powers of 10 and hence increasing it's value. To get it back to its original value we have to divide it as many times by 10, as we multiplied it. Dividing by a number is the same as multiplying by its reciprocal. So if we did the division by 10, [tex] n[/tex] times, it's like we divided it once [tex] 10^n [/tex] times, which is the same as mupliplying it [tex] 10^{-n} [/tex] times. Hence the exponent must be negative.
