Scientific Notation C3.1

Scientific Notation A number is written in scientific notation if it is written as the product of a coefficient n between 1 and 10 and an integer power of 10 (exponent). A number written in scientific notation has the form where 1 < n < 10 and r is an integer.

Use of scientific notation Express very small and very large numbers 2.0 x 108 instead of 200,000,000 3.5 x 10-7 instead of 0.00000035 Indicates the precision of a number What is meant if two cities are said to be separated by a distance of 3,000 miles?

What do we mean by 3,000 miles? A distance between 2,999 and 3001 miles? A distance between 2,990 and 3010 miles? A distance between 2,900 and 3100 miles? A distance between 2,000 and 4000 miles? Scientific notation allows us to express all these quantities with the precision or uncertainty being explicit; 3.000 x 103 or 3.00 x 103 or 3.0 x 103 or 3 x 103

Sample Problems Write the following in scientific notation to 2 sig. figs. Write the following in scientific notation to 4 sig. figs.

Sample Problems Write the following in scientific notation.

Properties for Exponents review If a is a real number, and r and s are integers, then

Properties for Exponents review If a is any nonzero real number, and r is a positive integer, then Note: Kg / L = Kg. L-1

Properties for Exponents review If a is any nonzero real number, and r and s are any two integers, then

Multiplication To multiply two numbers in scientific notation: Multiply the coefficients. Add the exponents. Examples: 3.0 x 104 x 2.0 x 104 = 6.0 x 108 4.0 x 10-3 x 3.0 x 105 = 12 x 102 = 1.2 x 103

Division To divide two numbers in scientific notation: 3.0 x 103 Divide the coefficients. Subtract the exponents. Examples: 9.0 x 105 = 3.0 x 102 4.5 x 104 = 9.0 x 105 3.0 x 103 5.0 x 10-2 0.50 x 10-1

Using a calculator Use a calculator to perform the indicated operation. Write your result in correct scientific notation. Enter 9.1 in your calculator. Press the key marked EXP or EE on your calculator. If this is written above another key, then you will have to press SHIFT or 2nd before pressing the EXP or EE key. Enter the value of the exponent. Press the times key. Enter 4.2 Repeat steps 2 and 3. Press Enter or = shows 0.3822 = 3.8 x 10-1

Addition -Then add the coefficients (0.35 x 106) + (6.4 x 106)= To add two numbers in scientific notation: (3.5 x 105) + (6.4 x 106) -Make the exponents the same -Then add the coefficients (3.5 x 105) + (6.4 x 106) = (0.35 x 106) + (6.4 x 106)= 6.75 x 106 = 6.8 x 106

Subtraction (6.4 x 106) - (3.5 x 105) = (64 x 105) - (3.5 x 105) = To subtract two numbers in scientific notation: (6.4 x 106) - (3.5 x 105) -Make the exponents the same -Then subtract the coefficients (6.4 x 106) - (3.5 x 105) = (64 x 105) - (3.5 x 105) = 60.5 x 105 = 6.1 x 106