Forces and Motion

Powers of Ten

100

101

102

103

etc.

1

10

100

1000

=

=

=

=

Speed and Velocity

Scientific Notation

Here is another way to make your calculations easier. Notice in the Mars problem that you had to write out 640,000,000 and then divide it by 260. Don’t you get tired of writing zeros and checking to make sure you got them all?

Scientists devised an easier way to write numbers and to multiply and divide them – its called scientific notation. Any number can be represented by two numbers that are multiplied together. For example, the travel distance to Mars is 6.4 x 108 km. The 6.4 are the first two digits, and the exponent 8 is the number of digits to the right of the decimal point following the 6. Count them – there are 8 digits. It is a lot easier to write is 6.4 x 108 than 640,000,000.

To solve the problem above, you convert the 260 to 2.6 x 102, and then divide 6.4 by 2.6 to get 2.5. To divide the part with exponents you just subtract the exponents: 108 /102 = 108-2 = 106. Now you put together the two pieces to get the answer: 2.5 • 106. Scientific notation makes hard problems easier – more information is given in the Appendix.