 # PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION

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PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION

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 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 x 10-4

Solution… x 10-6 2.37 x 10-6 x 10-4

Solution… x 10-4 x 10-4 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 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 x 105 2.0 x x 107 = x 107 = x 107 1. Make exponents of 10 the same 2. Subtract 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

(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) =

(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

(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) =