Mathematical Operations Using Numbers in Scientific Notation

Adding All numbers must be expressed in the same power of 10 (A x 10m) + (B x 10m)  (A + B) x 10m (1.234 x 10‾³) + (5.623 x 10‾3) = 1.234 + 5.623 6.857 = 6.857 x 10‾3 (answer is in correct sig figs)

Adding All numbers must be expressed in the same power of 10 (A x 10m) + (B x 10m)  (A + B) x 10m (2.2 x 10³) + (4.12 x 103) = Line up the decimals and add 2.2 x 10³ + 4.12 x 103 6.32 x 103 = 6.3 x 103 (round to correct sig figs)

When moving decimals: If you move the decimal to the right, add (-1) to the exponent If you move the decimal to the left, add (+1) to the exponent

10.85 X 10-2 need to move the decimal to the left so will add a (+1) = 10.85 X 10-2+1 = 1.085 X 10-1 If your result is: 0.233 x 102 need to move the decimal to the right so will add a (-1) = 0.233 x 102-1 = 2.33 X 101

1.234 Different Exponents (1.234 x 10‾³) + (5.623 x 10‾²) = Doesn’t matter which exponent you change (1.234 x 10‾³) + (56.23 x 10-2+-1=-3) = 57.464 x 10‾² 1.234 +56.23 57.464 x 10‾³ = 57.46 x 10‾³ = 5.746 x 10‾² (0.1234 x 10‾²) + (5.623 x 10‾²) = 5.746 x 10‾²

Addition (0.1234 x 10‾2) + (5.623 x 10‾²) = Doesn’t matter which exponent you change (0.1234 x 10‾²) + (5.623 x 10‾²) = 5.7464 x 10‾2 = 5.764 x 10‾2 OR (1.234 x 10‾³) - (56.23 x 10-2+-1=-3) = 57.464 x 10‾² 1.234 - 56.23 -57.464 x 10‾³ = -5.746 x 10‾²

Check your work! (1.234 x 10‾³) + (5.623 x 10‾²) = 0.001234 + 0.05623 = 0.001234 +0.05623 0.057464 = 5.746 x 10‾²

Subtracting 2000 X 104 – 5 X 104 = 1995 X 104 Need to round answer to correct sig figs! 1995 X 104 becomes 2000 X 104 Still not done! 2000 X 104 = move the decimal 3 places to the left and add “3” to the exponent 2000 X 104+3 = 2 x 107

Multiplying Multiply the decimal parts Add the exponents of 10s (A x 10m) x (B x 10n)  (A x B) x 10(m +n) (1.23 x 103) x (7.60 x 102) = (1.23 x 7.60) x 10 (3 + 2) = 9.348 x 10 5 = 9.35 x 10 5 (ROUND TO CORRECT SIG FIGS)

Example (4.16 x 103)(2 x 104) =

Dividing Divide the decimal parts Subtract the exponents (A x 10x)  (B x 10y)  (A  B) x 10(x-y) or A B 10(x-y) x

Example: (4.68 x 10-3) ÷ (4.00 x 10-5) 4.68 4.00 10 -3-(-5) = 1.17 x 102 x

Using Pre-determined Measurements in Calculations The value given in your calculation will influence the number of sig figs in your answer.

Page 90 - Classroom exercises