105 = 10 x 10 x 10 x 10 x 10 = 100,000 (5 zeros)
108 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 (8 zeros)
Notice that the number of zeros in the ordinary decimal expression is exactly equal to the power to which 10 is raised.
If the number is expressed in words, first write it down as an ordinary decimal number and then convert. Thus, "ten million" becomes 10,000,000. There are seven zeros, so in powers of ten notation ten million is written 107.
A number which is some power of 1/10 can also be expressed easily in scientific notation. By definition,
1/10 = 10-1 ("ten to the minus one power")
More generally, the expression "10-n" (where n is a whole number) means ( 1/10 )n. Thus
10-3 = ( 1 / 10 )3 = 1 / ( 10 x 10 x 10) = 1/1000
10-8 = ( 1 / 10 )8 = 1/100,000,000