PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

Review: M x 10n Scientific notation expresses a number in the form: n is an integer 1  M  10

IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 4 x 106 + 3 x 106 _______________ 7 x 106

IF the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged. 4 x 106 + 3 x 106 _______________ 7 x 106

If the exponents are NOT the same, we must move a decimal to make them the same.

4.00 x 106 4.00 x 106 + 3.00 x 105 + .30 x 106 4.30 x 106 Move the decimal on the smaller number!

A Problem for you… 2.37 x 10-6 + 3.48 x 10-4

Solution… 002.37 x 10-6 2.37 x 10-6 + 3.48 x 10-4

Solution… 0.0237 x 10-4 + 3.48 x 10-4 3.5037 x 10-4

Addition and subtraction Scientific Notation 2.0 x 102 + 3.0 x 103 1. Make exponents of 10 the same 2. Add 0.2 + 3 and keep the 103 intact The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same. 2.0 x 107 - 6.3 x 105 2.0 x 107 -.063 x 107 = 2.0-.063 x 107 = 1.937 x 107 1. Make exponents of 10 the same 2. Subtract 2.0 - .063 and keep the 107 intact

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION MULTIPLYING AND DIVIDING

Rule for Multiplication When multiplying with scientific notation: Multiply the coefficients together. Add the exponents. The base will remain 10.

(2 x 103) • (3 x 105) = 6 x 108

(9.2 x 105) x (2.3 x 107) = 21.16 x 1012 = 2.116 x 1013

(3.2 x 10-5) x (1.5 x 10-3) = 4.8 • 10-8

Rule for Division When dividing with scientific notation Divide the coefficients Subtract the exponents. The base will remain 10.

(8 • 106) ÷ (2 • 103) = 4 x 103

(3.402 x 105) ÷ (6.3 x 107) = 0.54 x 10-2

Please multiply the following numbers. (5.76 x 102) x (4.55 x 10-4) = (3 x 105) x (7 x 104) = (5.63 x 108) x (2 x 100) = (4.55 x 10-14) x (3.77 x 1011) = (8.2 x10-6) x (9.4 x 10-3) =

Please multiply the following numbers. (5.76 x 102) x (4.55 x 10-4) = 2.62 x 10-1 (3 x 105) x (7 x 104) = 2.1 x 1010 (5.63 x 108) x (2 x 100) = 1.13 x 109 (4.55 x 10-14) x (3.77 x 1011) = 1.72 x 10-2 (8.2 x10-6) x (9.4 x 10-3) = 7.71 x 10-8

Please divide the following numbers. (5.76 x 102) / (4.55 x 10-4) = (3 x 105) / (7 x 104) = (5.63 x 108) / (2) = (8.2 x 10-6) / (9.4 x 10-3) = (4.55 x 10-14) / (3.77 x 1011) =

Please divide the following numbers. (5.76 x 102) / (4.55 x 10-4) = 1.27 x 106 (3 x 105) / (7 x 104) = 4.3 x 100 = 4.3 (5.63 x 108) / (2 x 100) = 2.82 x 108 (8.2 x 10-6) / (9.4 x 10-3) = 8.7 x 10-4 (4.55 x 10-14) / (3.77 x 1011) = 1.2 x 10-25

Scientific Notation Makes These Numbers Easy 9.54x107 miles 1.86x107 miles per second