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 = 2716.54 ft

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

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

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

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

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

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

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

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

Independent practice

1) 4000.2 m + 500.375 m =

2) 0.3703 cm + 0.20 cm =

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

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

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=

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

Summary

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