Scientific Notation

What is scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise.

Why use scientific notation? For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form. Numbers expressed in scientific notation can be used in a computation with far greater ease.

Proper Scientific Notation consists of two parts: A number between 1 and 9.9999 . . . . A power of 10 N x 10x

Are these in proper scientific notation form? 23.98393 x 109 4.1 x 104 98920.188438 x 10-3 2.22221 x 1029 9.002 x 100 0.1103827493 x 102 NO YES NO YES YES NO

Changing standard form to scientific notation.

To change standard form to scientific notation… Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

Continued… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Example 1 Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108

Example 2 Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4

Practice 378000 b. 0.009340 c. 0.000000983 d. 1.9284 e. 34.903 3.78 x 105 9.340 x 10-3 9.83 x 10-7 1.9284 x 100 3.9403 x 101

Changing scientific notation to standard form.

To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

Example 3 Given: 5.093 x 106 Answer: 5,093,000 (moved 6 places to the right)

Example 4 Given: 1.976 x 10-4 Answer: 0.0001976 (moved 4 places to the left)

Practice a. 1.493 x 105 b. 2.908 x 10-4 c. 3.90284 x 102 149300 0.0002908 390.284

Doing Math with Numbers in Scientific Notation Addition/Subtraction Convert small number into same power of ten as larger Carry out operation Adjust to proper form if needed

Example 3.2 x 103 + 5.7 x 104 Step #1 Change smaller to larger Step #2 Carry out operation .32 x 104 + 5.7 x 104 = 6.02 x 104 Step #3 Adjust if needed Not needed

Doing Math with Numbers in Scientific Notation Mulitplication Multiply leading numbers Add exponents Adjust to proper form if needed

Example 3.2 x 103 times 5.7 x 104 Step #1 Multiply leading numbers Step #2 Add exponents 103 + 104 = 107 Step #3 Adjust if needed 18 x 107  1.8 x 108

Doing Math with Numbers in Scientific Notation Division Divide leading numbers Subtract exponents (N-D) Adjust to proper form if needed

Example 3.2 x 103 divided by 5.7 x 104 Step #1 Divide leading numbers 3.2 / 5.7 = 0.56 Step #2 Subtract exponents 103 - 104 = 10-1 Step #3 Adjust if needed 0.56 x 10-1  5.6 x 10-2