1. Significant Figures in measurements and calculations

2. significant figures objective
I can determine precision of a number using “sig figs”
I can calculate using the correct precision i.e. correct “sig figs”

3. Significant Figures in Measurements
What are Significant Figures?
Significant Figures convey important information about the precision of a measurement.
In measurements, Significant Figures are all the digits that can be known precisely in a measurement, plus a last estimated digit. .

4. Significant Figures in Measurements
In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated.
Volume in the graduated cylinder
__________ ml

5. Metric Ruler Sig Figs 13.30 cm
On a metric ruler, the smallest divisions are millimeters, 0.1 cm or 0.001m. Rarely does the object end neatly on one of the lines of the instrument, but that forces the use of measurement zeros.
13.30 cm
To indicate that the object being measured ends exactly at the third line after the 13, we must write cm. This indicates that, to our best estimation, the measurement does not extend into the hundredth of the centimeter.

6. Metric ruler sig figs 14.00 cm
If the object ends exactly at the 14 cm line, we must add two zeros to the end.
[Default]
[MC Any]
[MC All]

7. Metric ruler sig figs 12.85 cm
Most of the time, our measurements fall between the lines and, we must make agonizing estimates about where the measurement does fall.
[Default]
[MC Any]
[MC All]

8. Thermometer Sig figs -1.1 68.0 ______ oC ______ oC
In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated.

9. Triple beam balance sig figs
In measurements, the significant figures are all the digits that are known, plus a last digit that is estimated.
[Default]
[MC Any]
[MC All]
19.04 g

10. Rules for writing and reading sig figs
In order to present results with the proper precision, we need to know how many significant figures are present in each number we use in a calculation.
There are four basic rules:
The digits always count.
Zeroes between the digits always count.
Zeroes in the beginning of a number never count.
Zeroes at the end of a number count only if there is a written decimal point.

11. Rules for writing and reading sig figs
The digits always count.
Zeroes between the digits always count.
Zeroes in the beginning of a number never count.
Zeroes at the end of a number count only if there is a written decimal point.
Rule #1 examples: 24.7cm, cm, 714 cm
All have three sig figs

12. Rules for writing and reading sig figs
The digits always count.
Zeroes between the digits always count.
Zeroes in the beginning of a number never count.
Zeroes at the end of a number count only if there is a written decimal point.
Rule #2 Examples: 7003 cm, cm, cm
all have 4 sig figs

13. Rules for writing and reading sig figs
The digits always count.
Zeroes between the digits always count.
Zeroes in the beginning of a number never count.
Zeroes at the end of a number count only if there is a written decimal point.
Example: cm, 0.422cm, cm
all have 3 sig figs
Hey!!! You can get rid of these place holding zeros by using scientific notation
7.01x10-3cm x10-1cm x10-6cm

14. Rules for writing and reading sig figs
The digits always count.
Zeroes between the digits always count.
Zeroes in the beginning of a number never count.
Zeroes at the end of a number count only if there is a written decimal point.
Rule 4 Examples: cm, mm, mm
All have 4 sig figs
Tricky Rule 4 Examples: the zeros in 300cm, 7000km and 210m are not significant
Ambiguity (doubt, uncertainty) about precision can be avoided by using scientific notation 3.00x102cm x103km 2.1x102m

15. Rules for writing and reading sig figs
Two situations have unlimited sig figs
a) counting
example: there are 28 desks in the classroom
b) defined quantities
example: 60minutes = 1 hour
1000 grams = 1 kilogram
7 days = 1 week

16. Enter answers in your notes too!! 1. Sig figs in 31.45 mL ?1 2 3 4 5
unlimited
31.45 mL
Rule 1: The digits always count.
[Default]
[MC Any]
[MC All]

17. Enter answers in your notes too!! 2. Sig figs in 150.53 g ?1 2 3 4 5
unlimited mL
Rule 2: Zeroes between the digits always count.
[Default]
[MC Any]
[MC All]

18. Enter answers in your notes too!! 3. Sig figs in 40.00 mL ?1 2 3 4 5
unlimited
40.00 mL
Rule 4: Zeroes at the end of a number (trailing zeros) count only if there is a written decimal point.
Has NOTHING to do with where the decimal is located !!!
[Default]
[MC Any]
[MC All]

19. Enter answers in your notes too!! 4. Sig figs in 0.056 mL ?1 2 3 4 5
unlimited
0.056 mL
Rule 3: Zeroes in the beginning of a number never count.
i.e. leading zeros do not count
[Default]
[MC Any]
[MC All]

20. Enter answers in your notes too!! 5. Sig figs in 10.10 g ?1 2 3 4 5
unlimited
[Default]
[MC Any]
[MC All]

21. Enter answers in your notes too!! 6. Sig figs in 1.5 L ?1 2 3 4 5
unlimited
[Default]
[MC Any]
[MC All]

22. Enter answers in your notes too!! 7. Sig figs in 8 yard TD pass?1 2 3 4 5
unlimited
[Default]
[MC Any]
[MC All]

23. Enter answers in your notes too!! 8. Sig figs in 220 miles to Dallas1 2 3 4 5
unlimited
220 miles
Rule 4: Zeroes at the end of a number (trailing zeros) count only if there is a written decimal point.
Has NOTHING to do with where the decimal is located !!!
[Default]
[MC Any]
[MC All]

24. Enter answers in your notes too!! 9. Sig figs in 12 donuts in a dozen?1 2 3 4 5
unlimited
There are always exactly 12 in a dozen.
Defined quantities and counting items have unlimited sig figs.
[Default]
[MC Any]
[MC All]

25. Practice 31.45mL has 4 sig figs 150.53g has 5 sig figs
0.056 seconds has 2 sig figs
10.10g has 4 sig figs
1.5L has 2 sig figs
8 yard touchdown pass has 1 sig fig
220 miles to Dallas has 2 sig figs
12 donuts in a dozen has unlisig figs

26. Practice 31.45mL has 4 sig figs 150.53g has 5 sig figs
0.056 seconds has 2 sig figs
10.10g has 4 sig figs
1.5L has 2 sig figs
8 yard touchdown pass has 1 sig fig
220 miles to Dallas has 2 sig figs
12 donuts in a dozen has unlimited sig figs

27. Significant Figures in Calculations
Multiplication and Division
round to the same number of significant figures as the measurement with the least number of significant figures
8.4 meters has two significant figures
meters
÷ meters
meter
= 0.29 meter or 2.9×10-1 meter
An answer cannot be more precise than the least precise measurement from which it was calculated.

28. Significant Figures in Calculations
Addition and Subtraction
Convert numbers to same exponent and align the decimal points, then
Round to the same number of decimal places as the least number of decimal places.
meters
meters
meters
meters
349.0 meters has the least number of digits (one) to the right of the decimal point.
Thus the answer must be rounded to one digit after the decimal point.
The correct rounded answer is meters or X 102 meters

29. Significant Figures in Calculations
What is the calculated area of your college dorm room to the correct number of significant figures?
16 feet
11 feet
An answer cannot be more precise than the least precise measurement from which it was calculated.
Once you know the number of significant figures your answer should have, you must round to that many digits, counting from the left.

30. Professor Harris reports his results to the correct number of sig figs.

31. Practice:
L + 9.4L 2. 20s s g X 7.000mL x102g X 8.000mL g / 3.12L g / 3.12L

32. Practice: answers with sigfigs underlined
L + 9.4L = = 14.7 L s s = 15.48s = 15s g X mL = 840 = 8.4x102 gmL x102g X 8.000mL = 960. gmL or 9.60x102 gmL g / 3.12L = = 321 or 3.21x102 g/L g / 3.12L = = 300 or 3x102 g/L

33. Another interesting defined quantity
The speed of light (usually denoted c) is a physical constant.
For much of human history, it was not known whether light was transmitted instantaneously or simply very quickly.
Its value is now defined to be exactly 299,792,458 meters per second. It has unlimited sigfigs!!
299,792, …….…
x 108 in scientific notation
How did they do that?
In 1983, the meter was redefined in the International System of Units (SI) as the distance traveled by light in vacuum in 1⁄299,792,458 of a second.
As a result, the value of c in meters per second is now fixed exactly by the definition of the meter.