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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