significant digits objective: state and apply the rules for + and - with sig figs
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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 ExampleMake 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 exampleMath class: 2716.54 ft + 984.252 ft = 3700.792 ft
Physics class:2716.54 2 decimal places984.252 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 time1 partner can read the question, 1
partner can give the answerIf 1 partner understands, help
the other partner learn the steps
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Example with your partner500.99 g + 101.0 g =
500.99 g + 101.0 g = 601.99 g
500.99 2 decimal places101.0 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 Example350.85 kg + 400.0 kg
350.85 kg + 400.0 kg = 750.85 kg
350.85 2 decimal places400.0 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 figsIf 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 same3.45 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 Partner3.25 m + 6.5 m = 3.25 m + 6.5 m = 9.75 m
3.25 2 decimal places6.5 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 Example4.0015 cm + 6.00 cm = 4.0015 cm + 6.00 cm = 10.0015 cm
4.0015 4 decimal places6.00 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 place500.375 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 Practice5.33 cm + 6.020 cm= 3.456 kg – 2.455 kg=
5.5 s – 2.500 s=
(3.0 x 104) m - (2.0 x 101) m=
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Practice - Answers
5.33 + 6.020 = 11.350 11.35 cm
3.456 – 2.455= 1.001 1.001 kg5.5 – 2.500 =3.000 3.0 s (3.0 x 104) - (2.0 x 101) = 2.998
x 104 3.0 x 104 m
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Summary
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