PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

Review: From our like term investigation: Values we could add/subtract without adjustment Values we could NOT add/subtract without adjustment

Adding/Subtracting SN IF the exponents are the same, we simply add or subtract the coefficient and bring the base of ten with the exponent down unchanged. 4 x 106 + 3 x 106 _______________ 7 x 106

Adding/Subtracting SN If the exponents are NOT the same, we must move a decimal to make them the same. 4 x 106 + 3 x 105 It doesn’t matter what exponent you change, but changing the smaller one keeps your final answer in scientific notation

Determine which of the numbers has the smaller exponent. Change this number by moving the decimal place to the left and raising the exponent, until the exponents of both numbers agree. Note: that this will take the lesser number out of scientific notation.

4.00 x 106 4.00 x 106 + 3.00 x 105 + .30 x 106 Move the decimal on the smaller number to the left and raise the exponent ! Note: This will take the lesser number out of scientific notation.

This allows them to be added/subtracted easily. Now that both numbers have common exponents with a base of 10, they are like terms. This allows them to be added/subtracted easily. 2. Add or subtract the coefficients as needed to get the new coefficient. 3. The answer’s exponent will be the exponent that both numbers have in common.

4.00 x 106 4.00 x 106 + 3.00 x 105 + .30 x 106 4.30 x 106 Add or subtract the coefficients as needed to get the new coefficient. The exponent will be the exponent that both numbers share.

Make sure your final answer is in the specified form, either scientific notation or standard form. If it is not, convert it to the correct form!

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

Solution… 2.37 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

PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION MULTIPLYING AND DIVIDING

Exponent Review: Simplify each expression. The rule for simplifying exponents when multiplying two expressions is ______________ the exponents. The rule for simplifying exponents when dividing two expressions is ______________ the exponents. For the coefficients, or numbers in front of the variables, you ___________ or _____________ like normal.     add subtract multiply divide Numbers in scientific notation are expressions too! Therefore, we’re going to use all the rules we already know to complete operations on numbers in scientific notation.

When multiplying with scientific notation: Multiply the coefficients together. Add the exponents because they have the same base. The base will remain 10. Make sure you answer is in correct scientific notation.

(2 x 103) • (3 x 105) = 6 x 108

((9.2 x 105)(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 x 10-8

(4.6x108) (5.8x106) =26.68x1014 Notice: What is wrong with this example? Although the answer is correct, the number is not in scientific notation. To finish the problem, move the decimal one space left and increase the exponent by one. 26.68x1014 = 2.668x1015

When dividing with scientific notation Divide the coefficients Subtract the exponents because they have the same base. The base will remain 10. Make sure you answer is in correct scientific notation.

(8 • 106) ÷ (2 • 103) = 4 x 103

(1.6 x 1014) (4 x 108) .4 x 106 4 x 105

Please multiply the following numbers. 1. (5.76 x 102) x (4.55 x 10-4) = 2. (3 x 105) x (7 x 104) = 3. (5.63 x 108) x (2 x 100) = 4. (4.55 x 10-14) x (3.77 x 1011) = 5. (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