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

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

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.”

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

Engineering example Burj Khalifa 160 stories tall = ft

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

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

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

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

Class Example kg kg kg kg = kg  2 decimal places  1 decimal place Lowest # of decimal places = 1  I need to round the answer to 1 dec. place kg  kg

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

Example with Partner 3.25 m m = 3.25 m 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

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

Independent practice 1) m m = 2) cm cm =

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

Independent Practice - Answers cm 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

Independent Practice 5.33 cm cm= kg – kg= 5.5 s – s= (3.0 x 10 4 ) m - (2.0 x 10 1 ) m=

Practice - Answers =  cm – 2.455=  1.001kg 5.5 – =3.000  3.0 s (3.0 x 10 4 ) - (2.0 x 10 1 ) = x 10 4  3.0 x 10 4 m

Summary

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