Powers of Ten and Scientific Notation Scientists need to make measurements of all sorts of objects and quantities, which range from the very tiny to the immensely large. For example, let's look at two different distance measurements, both in units of meters. An astronomer measures the diameter of a galaxy to be about 20,000,000,000,000,000,000,000 meters. That's a "2" followed by 22 zeroes! On the other hand, a nuclear physicist measures the diameter of an atomic nucleus to be about 0.000000000000002 meters. That's 14 zeroes after the decimal point, before reaching the "2" in the 15th decimal place! How can we condense these measurements into a more readable format? And how can we make understandable comparisons between very large and very small numbers? To do this, we need to understand powers of ten and scientific notation. Part 1 of 5 - Introducing Scientific Notation Introducing Scientific Notation The Moon is roughly 3,500 kilometers (3,500,000 meters) in diameter. A mosquito might span 3.5 millimeters (0.0035 meters) in length. How many mosquitoes, placed end to end, would span the width of the Moon? Simple: divide the Moon's diameter by the length of a mosquito! But even if our calculator had enough room for all those zeros, you might hit the zero key too few times-or too many. Better to use scientific notation. Scientific notation expresses any number in two parts. The first part is a regular number between 1 and 10. Like most sources, we'll call this the coefficient. (Some books and web sites may call it the argument, significand, or mantissa.) The next part is 10 raised to an integer power: 10", with n taking on any integer value, negative or positive (or zero)-though most calculators only allow for values between -99 and +99. The number n is called the "power of ten" or exponent. In other words, it can be explained thusly. Scientific Notation C X 10 1 s c