Why do we have to learn about Sig Figs? · 2019-09-13 · Sig Figs tell you what place to round...

Sig Figs tell you what place to round your

answers to.

Your final measurement (answer) can never be

more precise than your starting measurement.

To understand that idea, we will discuss

accuracy vs. precision

Why do we have to learn

about Sig Figs?

Accuracy & Precision

Two important points in measurement

THE BIG CONCEPT

1. Accuracy –indicates the closeness of the

measurements to the true or accepted value.

Beware of Parallax – the apparent shift in

position when viewed at a different angle.

2. Precision - The closeness of the results to

others obtained in exactly the same way.

Accuracy vs. Precision

High Accuracy

High Precision

High Precision

Low Accuracy

Three targets with three arrows each to shoot.

Can you hit the bull's-eye?

Accurate and precise

Precise but not accurate

Neither accurate nor precise

How do they compare?

Can you define accuracy vs. precision?

Example: Accuracy

Who is more accurate when measuring a book

that has a true length of 17.0 cm?

Susan:

17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm

Amy:

15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

Example - Precision

Which set is more precise?

A. 18.2cm , 18.4cm , 18.3cm

B. 17.9cm , 18.3cm , 18.8cm

C. 16.8cm , 17.2cm , 19.4cm

Recording Measurements

Every experimental measurement has

a degree of uncertainty.

The degree of uncertainty depends

on the tool you are using.

The volume, at the right is certain in

the 10’s place, Greater than 10ml

and less than 20ml

The 1’s digit is also certain, greater

than 17ml and less than 20ml.

A best guess is needed for the tenths

place.

Known + Estimated Digits

In 2.77 cm…

• Known digits 2 and 7 are 100% certain

• The third digit 7 is estimated (uncertain)

• In the reported length, all three digits

(2.77 cm) are significant including the

estimated one

Always estimate ONE place past the

smallest mark!

11.50mL

Learning Check

. l8. . . . I . . . . I9. . . . I . . . . I10. . cm

What is the length of the line?

1) 9.31 cm

2) 9.32 cm

3) 9.33 cm

How does your answer compare with your

neighbor’s answer? Why or why not?

Zero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?

First digit 5.?? cm

Second digit 5.0? cm

Last (estimated) digit is 5.00 cm

Precision and Instruments

Do all measuring devices have the same amount

of precision?

You indicate the precision of the

equipment by recording its

Uncertainty

Ex: The scale on the left has an

uncertainty of (+/- .1g)

Ex: The scale on the right has an

uncertainty of (+/- .01g)

Below are two measurements of the

mass of the same object. The same

quantity is being described at two

different levels of precision or

certainty.

Checkpoint

Complete the Accuracy and Precision

Worksheet with a partner.

Significant Figures

In Measurements

Significant Figures

The significant figures in a measurement include all

of the digits that are known, plus one last digit

that is estimated.

The numbers reported in a measurement are limited by the measuring tool.

How to Determine Significant

Figures in a Problem

Use the following rules:

Rule #1

Every nonzero digit is significant

Examples:

24m = 2

3.56m = 3

7m = 1

Rule #2 – Sandwiched 0’s

Zeros between non-zeros are

significant

Examples:

7003m = 4

40.9m = 3

Rule #3 – Leading 0’s

Zeros appearing in front of non-zero digits are not significant

• Act as placeholders

Examples:

0. 24m = 2

0.453m =

0.00234m =

0.02034m =

3 3

4

Rule #4 – Trailing 0’s with

Decimal Points

Zeros to the right of a decimal and after a

whole number are significant.

Examples:

43.00g = 4

1.010g = 4

1.50g = 3

0.00020g = 2

0.0002g = 1

2,020g = 3

Performing Calculations

with Significant Figures

Rule: When adding or subtracting

measured numbers, your answer

cannot be more precise than the

least precise measurement.

Only count the Sig Figs that come

after the decimal.

Adding and Subtracting

2.45 cm + 1.2 cm = 3.65 cm,

Round off to 3.7 cm

7.432 cm + 2 cm = 9.432 cm

Round to 9cm

Multiplication and Division

Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

Count all of the Sig figs in the entire number.

Examples

56.78 cm x 2.45cm = 139.111 cm2

Round to 139cm2

75.8 cm x 9.6 cm = ?

State the number of significant figures in each

of the following:

A. 0.030 m 1 2 3

B. 4.050 L 2 3 4

C. 0.0008 g 1 2 4

D. 3.00 m 1 2 3

E. 2,080,000 bees 3 5 7

Learning Check

Learning Check

A. Which answer(s) contain 3 significant figures?

1) 0.4760 2) 0.00476 3) 4760

B. All the zeros are significant in

1) 0.00307 2) 25.300 3) 2.050 x 103

C. 534,675 rounded to 3 significant figures is

1) 535 2) 535,000 3) 5.35 x 105

Learning Check

In which set(s) do both numbers contain the

same number of significant figures?

1) 22.0 m and 22.00 m

2) 400.0 m and 40 m

3) 0.000015 m and 150,000 m