why do we have to learn about sig figs? · 2019-09-13 · sig figs tell you what place to round...
TRANSCRIPT
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