1. Significant digits Objective: State and apply the rules for + and - with sig figs

2. Significant digits “Which digits are giving me information about how precise my measurement is?”

3. Rules for sig figs in calculations: Addition and subtraction: BIG IDEA: the answer can only be as precise as the least precise original measurement “You’re only as strong as your weakest link.”

4. Addition and subtraction: More precision is given by _________? More precision is given by more decimal places. What does this mean? Our answer has the same number of decimal places as the LOWEST # of decimal places in the measurement

5. Engineering example Burj Khalifa 160 stories tall = 2716.54 ft

6. Engineering Example Make a tower that is 10 stories taller than the Burj Khalifa ◦ Make a tower that is 984.252 ft taller What is the height of this new tower? 2716.54 ft + 984.252 ft

7. Engineering example Math class: 2716.54 ft + 984.252 ft = 3700.792 ft Physics class: 2716.54  2 decimal places 984.252  3 decimal places Lowest # of decimal places = 2  I need to round the answer to 2 dec. places 3700.792 ft  3700.79 ft

8. Example with Your Partner Reminders on how to work with a partner: Working on the same problem at the same time 1 partner can read the question, 1 partner can give the answer If 1 partner understands, help the other partner learn the steps

9. Example with your partner 500.99 g + 101.0 g = 500.99 g + 101.0 g = 601.99 g 500.99  2 decimal places 101.0  1 decimal place Lowest # of decimal places = 1  I need to round the answer to 1 dec. place 601.99 g  602.0 g

10. Class Example 350.85 kg + 400.0 kg 350.85 kg + 400.0 kg = 750.85 kg 350.85  2 decimal places 400.0  1 decimal place Lowest # of decimal places = 1  I need to round the answer to 1 dec. place 750.85 kg  750. 8 kg

11. Rules of rounding for sig figs If there is a 5 in the first place after the digit you are rounding to: ◦ If the rounding digit is odd, round it up 3.35  3 is odd so I round up to 3.4 ◦ If the rounding digit is zero or even, it stays the same 3.45  4 is even so I round to 3.4 Why do we do this? ◦ Scientists made this rule to account for any rounding errors that occur during calculations

12. Example with Partner 3.25 m + 6.5 m = 3.25 m + 6.5 m = 9.75 m 3.25  2 decimal places 6.5  1 decimal place Lowest # of decimal places = 1  I need to round the answer to 1 dec. place 9.75 m  7 is odd so I round up to 9.8 m

13. Class Example 4.0015 cm + 6.00 cm = 4.0015 cm + 6.00 cm = 10.0015 cm 4.0015  4 decimal places 6.00  2 decimal place Lowest # of decimal places = 2  I need to round the answer to 2 dec. places 10.0015 cm  10.00 cm

14. Independent practice 1) 4000.2 m + 500.375 m = 2) 0.3703 cm + 0.20 cm =

15. Independent Practice - Answers 4000.2 m + 500.375 m = 4500.575 m 4000.2  1 decimal place 500.375  3 decimal places Lowest # of decimal places = 1  I need to round the answer to 1 dec. place 4500.575 m  4500.6 m

16. Independent Practice - Answers 0.3703 cm + 0.20 cm =.5703 cm.3703  4 decimal places.20  2 decimal places Lowest # of decimal places = 2  I need to round the answer to 2 dec. place.5703 cm .57 cm

17. Independent Practice 5.33 cm + 6.020 cm= 3.456 kg – 2.455 kg= 5.5 s – 2.500 s= (3.0 x 10 4 ) m - (2.0 x 10 1 ) m=

18. Practice - Answers 5.33 + 6.020 = 11.350  11.35 cm 3.456 – 2.455= 1.001  1.001kg 5.5 – 2.500 =3.000  3.0 s (3.0 x 10 4 ) - (2.0 x 10 1 ) = 2.998 x 10 4  3.0 x 10 4 m

19. Summary

20. Exit Ticket