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Significant digits Objective: State and apply the rules for + and - with sig figs
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Significant digits “Which digits are giving me information about how precise my measurement is?”
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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.”
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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
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Engineering example Burj Khalifa 160 stories tall = 2716.54 ft
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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
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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
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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
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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
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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
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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
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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
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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
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Independent practice 1) 4000.2 m + 500.375 m = 2) 0.3703 cm + 0.20 cm =
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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
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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
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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=
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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
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Summary
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Exit Ticket
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