Section 8.5 Scientific Notation

So we use scientific notation. Positive exponents can create very large numbers, and negative exponents create very small numbers. It can take a long time to write out numbers like 1,000,000,000,000,000,000,000,000,000 So we use scientific notation.

a x 10n A number is in scientific notation if it is in the form where n is an integer and ex: -3.4 x 1017 ex: 7.89 x 10-12 Note: 43 x 107 is not in scientific notation. Why not? *Because 43 is not between 1 and 10. We should use 4.3 and make the exponent 8 instead of 7.

Working with Scientific Notation: A positive exponent means the number is big and a negative exponent means the number is small. Each time you increase the exponent by 1, you are multiplying by 10. Multiplying by 10 moves the decimal one place to the right. Each time you decrease the exponent by 1, you are dividing by 10. Dividing by 10 moves the decimal one place to the left.

Examples: Convert to standard notation: = 38,000 Move the decimal 4 places to the right. Move the decimal 4 places to the left. = .000762 Move the decimal 8 places to the right. = 400,000,000 Move the decimal 5 places to the left. = -.000008

Examples: Convert to scientific notation: 5.) 689,000,000 6.89 There are eight digits after the decimal. 6.) 0.00034 3.4 There are 4 digits before Step 1: Place a decimal point after the first number. Step 2: Count the number of digits on the other side of the new decimal place. Step 3: The number of digits is the exponent. If the original number is a decimal, it is a negative exponent. Step 4: Multiply your number by 10 to the exponent.

Homework 8.5 (Due at the beginning of next class.) Page 388 (1 – 29 odds, 33 – 45 odds) Quiz next class (Friday 2/11) Quiz will cover 8.3-8.5