Scientific Notation

The mass of one gold atom is .000 000 000 000 000 000 000 327 grams. Scientific Notation is used to express the very large and the very small numbers so that problem solving will be made easier. Examples: The mass of one gold atom is .000 000 000 000 000 000 000 327 grams. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms.

How to Use Scientific Notation In scientific notation, a number in put into a general form: # x 10 n # = number (1.00-9.99) n = exponent (can be + or – )

For example: 4.50 x 103 The coefficient is _________. 4.50 The number 4,500 is written in scientific notation as ________________. The coefficient is _________. 4.50 The coefficient must be a number that fits between 1.00 and 9.99. The power of 10 or exponent in this example is ______. 3 The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500. For this class, we will report all scientific notation to 2 decimal places.

1. Move the decimal to the right of the first non-zero number. To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the number was a large #, exp = positive. It if was a small #, exponent = negative.

Put these numbers in scientific notation. PROBLEMS ANSWERS 0.000120 1000 0.0100 12 0.987 596 0.000 000 700 1,000,000 0.001257 987,653,000,000 1.20x10-4 1.00x103 1.00x10-2 1.20x101 9.87x10-1 5.96x102 7.00x10-7 1.00x106 1.26x10-3 9.87x1011

Taking #’s Out of Sci. Not. THINK OF A NUMBER LINE! If the exponent is positive, move the dec. right! If the exponent is negative, move the dec. left!

EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMS ANSWERS 4.90 X 102 3.75 X 10-2 5.95 X 10-4 9.46 X 103 3.87 X 101 7.10 X 103 8.20 X 10-5 490 0.0375 0.000595 9460 38.70 7100 0.000082