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Name __________________________ Period ______ Scientific Notation Scientists often deal with very small and very large numbers, which can lead to a lot of confusion when counting zeros! We have learned a way to express these numbers as powers of 10 in order to decrease their size when written. Scientific notation takes the form shown here: n M x 10 In this example “M” is always a single digit number (not zero!) and “n” represents the number of decimal places that were moved. Example 1: Convert 1,500,000. to scientific notation. - Move the decimal point 6 spaces to the left so it is between the 1 and 5 to get… 6 o 1.5 x 10 (positive exponent!) Example 2: Convert 0.00025 to scientific notation. - Move the decimal 4 places to the right so it is between the 2 and the 5 to get… -4 o 2.5 x 10 (negative exponent!) Convert the following to scientific notation: 1) 0.005 _____________________ 6) 0.25 _____________________ 2) 5,050 _____________________ 7) 0.025 _____________________ 3) 0.0008 _____________________ 8) 0.0025 _____________________ 4) 1,000 _____________________ 9) 500 _____________________ 5) 1,000,000 _____________________ 10) 5,000 _____________________ Convert the following to standard notation: 3 1) 1.5 x 10 _____________________ 6) 0.25 _____________________ 2) 5,050 _____________________ 7) 0.025 _____________________ 3) 0.0008 _____________________ 8) 0.0025 _____________________ 4) 1,000 _____________________ 9) 500 _____________________ 5) 1,000,000 _____________________ 10) 5,000 _____________________ Calculations Using Significant Figures When multiplying numbers in scientific notation, multiply the first part of the number (mantissa) and add the exponents: 2 6 Example 1: (3.0 x 10 ) x (2.5 x 10 ) - Multiply 3.0 x 2.5 = 7.5 - Add 2 + 6 = 8 - 8 Answer = 7.5 x 10 When dividing numbers in scientific notation, divide the first part of the number and subtract exponents. 6 2 Example 2: (9.0 x 10 ) / (4.5 x 10 ) - Divide 9.0 / 4.5 = 2.0 - Subtract 6 - 2 = 4 - 4 Answer = 2.0 x 10 Perform the following calculations and show all answers in scientific notation! 3 5 6) (4 x 10 ) / (1 x 10 ) 8 6 7) (7.6 x 10 ) x (8.2 x 10 ) 1) (1.5 x 10 ) x (3.5 x 10 ) 2) (2.0 x 10 ) x (2.0 x 10 ) 5 -3 -3 6 2 8) (8.5 x 10 ) / (2.5 x 10 ) 4 3 9) (7.0 x 10 ) x (7.0 x 10 ) 3) (6.2 x 10 ) / (3.1 x 10 ) 4) (5.0 x 10 ) / (2.5 x 10 ) 7 -5 5) (6.8 x 10 ) x (2.2 x 10 ) -8 -4 11 -5 -3 -11 -9 10) (1.3 x 10 ) / (2.6 x 10 )