Scientific Notation and Computations

by Eric Feigelson, Professor of Astronomy & Astrophysics

Penn State University

1. The exponent shows how many zeros are present to the left of the decimal point.

Examples:: 200 = 200. = , 5/1000 = 0.005 = .

2. Notation:

Examples:: 1 millimeter = micrometers = meters = kilometers; The mass of the Sun is grams = kilograms

3. To multiply in scientific notation, multiply the numbers in front, add the exponents, and (if necessary) change exponent so the number in front is between 1 and 10.

Examples:: What is the mass of a galaxy with Suns?; Answer: grams = grams.

4. To divide in scientific notation, divide the numbers in front, subtract the exponents, and (if necessary) change exponent so the number in front is between 1 and 10.

Examples:: How many atoms are in your body if your mass is 60 kilograms and a typical atomic mass is kilograms?; Answer: = atoms.; How long would it take for the Space Shuttle to reach the nearest star if it travels at 6 kilometers/second and the star is meters away?; Answer: meters / ( meters/second) = seconds = seconds. Note the change of units between kilometers and meters.

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Last updated: Aug 17, 1996 Matthew A. Bershady