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Mathematical Operations Using Numbers in Scientific Notation

Mathematical Operations Using Numbers in Scientific Notation. Adding. All numbers must be expressed in the same power of 10 (A x 10 m ) + (B x 10 m )  (A + B) x 10 m If exponents are already the same… (2.2 x 10³) + (4.12 x 10 3 ) = 2.2 x 10³ + 4.12 x 10 3

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Mathematical Operations Using Numbers in Scientific Notation

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  1. Mathematical Operations Using Numbers in Scientific Notation

  2. Adding All numbers must be expressed in the same power of 10 (A x 10m) + (B x 10m)  (A + B) x 10m If exponents are alreadythe same… (2.2 x 10³) + (4.12 x 103) = 2.2 x 10³ + 4.12 x 103 6.32 x 103 = 6.3 x 103 (round to correct sig figs)

  3. Adding All numbers must be expressed in the same power of 10 (A x 10m) + (B x 10m)  (A + B) x 10m If exponents are already the same… (1.51 x 10‾2) + (9.34 x 10‾2) = 1.51 + 9.34 10.85 x 10‾2 needs to be converted to proper scientific notation or 1.085 x 10‾1 (answer is in correct sig figs)

  4. To put 10.85 x 10‾2 in proper scientific notation we need to move the decimal and change the exponent. So :If you move the decimal to the right, add (-1) to the exponentIf you move the decimal to the left, add (+1) to the exponent

  5. 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

  6. 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

  7. Addition (1.234 x 10‾³) + (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 = 5.746 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

  8. 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

  9. 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

  10. 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)

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

  12. 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

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

  14. Using Pre-determined Measurements in CalculationsIf a value given is a measurement and is used in a calculation, it will influence the number of sig figs in your answer.

  15. Using Pre-determined Measurements in Calculations Values of gravity could be: 6.7 X 10-11 N m2 kg-2 6.672 X 10-11 N m2 kg-2 6.67 X 10-11 N m2 kg-2 All three values represent the force of gravity on earth but they are expressed with a different degree of accuracy. Therefore, where this value appears in a calculation, it would influence the number of significant digits used in the final answer.

  16. Classroom exercises

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