The first thing to learn is how to convert numbers back and forth between scientific notation and ordinary decimal notation. The expression "10n", where n is a whole number, simply means "10 raised to the nth power," or in other words, a number gotten by using 10 as a factor n times:
<span><span>105 = 10 x 10 x 10 x 10 x 10 = 100,000 (5 zeros)</span><span>108 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 (8 zeros)</span></span>
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,
<span>1/10 = 10-1 ("ten to the minus one power")</span>
More generally, the expression "10-n" (where n is a whole number) means ( 1/10 )n. Thus
<span><span>10-3 = ( 1 / 10 )3 = 1 / ( 10 x 10 x 10) = 1/1000</span><span>10-8 = ( 1 / 10 )8 = 1/100,000,000</span></span>
