Download presentation

Presentation is loading. Please wait.

Published byJewel Madlyn Mosley Modified over 8 years ago

1
Mathematical Operations Using Numbers in Scientific Notation

2
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 6.32 x 10 3 = 6.3 x 10 3 (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 exponent If 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 10 2 need to move the decimal to the right so will add a (-1) = 0.233 x 10 2-1 = 2.33 X 10 1

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 10 4 – 5 X 10 4 = 1995 X 10 4 Need to round answer to correct sig figs! 1995 X 10 4 becomes 2000 X 10 4 Still not done! 2000 X 10 4 = move the decimal 3 places to the left and add “3” to the exponent 2000 X 10 4+3 = 2 x 10 7

10
Multiplying Multiply the decimal parts Add the exponents of 10s (A x 10 m ) x (B x 10 n ) (A x B) x 10 (m +n) (1.23 x 10 3 ) x (7.60 x 10 2 ) = (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 10 3 )(2 x 10 4 ) =

12
Dividing Divide the decimal parts Subtract the exponents (A x 10 x ) (B x 10 y ) (A B) x 10 (x-y) or A B x 10 (x-y)

13
Example: (4.68 x 10 -3 ) ÷ (4.00 x 10 -5 ) 4.68 4.00 x 10 -3-(-5) = 1.17 x 10 2

14
Using Pre-determined Measurements in Calculations If 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 m 2 kg -2 6.672 X 10 -11 N m 2 kg -2 6.67 X 10 -11 N m 2 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

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google