Unit 0: Working as a Scientist –Significant Figures
AGENDA:
•DO NOW
•NOTES
•WHITE BOARDING
•LAB
GOAL:
I can properly record and calculatedata with proper significant figures bytaking notes, practicing, andperforming a lab.
Homework: SignificantFigures Practice
Do Now –
What is the difference between the values of3, 3.0, and 3.00
Monday
Tuesday
Wednesday
Thursday
Friday
UncertaintyandMeasurement
UncertaintyandMeasurement
SignificantFigures
SignificantFigures
ACT Fridays
Significant Figures
Instruments are only so precise.
The number of digits reported are considered significant figures.
There are rules for determining the number of significant figures.
RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG
1
6
17
183
34.25
12,375
2
3
4
Rules for Significant Figures
1. Non-zero numbers are always significant.
Ex. 72.3 has 3 significant figures.
RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG
1
6
17
183
34.25
12,375
2
10
1500
103
5001
12,305
3
4
Rules for Significant Figures
1. Non-zero numbers are always significant.
Ex. 72.3 has 3 significant figures.
2. Zeros between non-zero numbers are alwayssignificant.
Ex. 60.5 has 3 significant figures.
RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG
1
6
17
183
34.25
12,375
2
10
1500
103
5001
12,305
3
50
50.
125,000
12.00
12.000
4
Rules for Significant Figures
1. Non-zero numbers are always significant.
Ex. 72.3 has 3 significant figures.
2. Zeros between non-zero numbers are alwayssignificant.
Ex. 60.5 has 3 significant figures.
3.Zeros before (to the left of) non-zero numbersare not significant.
Ex. 0.0253 has 3 significant figures
RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG
1
6
17
183
34.25
12,375
2
10
1500
103
5001
12,305
3
50
50.
125,000
12.00
12.000
4
0.000001
0.0068
502
502.0
502,340,000
4. All Zeros after (to the right of) non-zeronumbers are significant IF there is a decimalpoint in the number.
Ex. 123.00 5 significant figures (decimal)
Ex. 12,000 2 significant figures (no decimal)
Ex. 120.0 4 significant figures (decimal)
Ex. 12,000. 5 significant figures (decimal)
Let’s try some together….
How many significant digits are in these numbers?
1.35 g
2.3.57 m
3.3.507 km
4.0.0035 kg
5.2406 L
6..0004 m
7.240.00 g
8.20.04080 g
How did you do?
1.35g2
2.3.57m3
3.3.507km4
4.0.0035kg2
5.2406 L4
6..0004m1
7.240.00 g5
8.20.04080 g7
White Boards and Sig Figs!
Write down your answer on the white board and holdit up when you think that you have the answer!
1.3 x 102
2
0.00002
1
4.521 x 10-4
4
230
2
0.002300
4
302.00
5
Rounding Numbers
Often times your calculator will give you more digits than necessary. Inthese cases you will round. Let try a few.
1. Round 3.515014 to 5 significant figures.
= 3.5150
2. Round 3.5150 to 3 significant figures
= 3.52
3. Round 3.52 to 1 significant figure
= 4
4. Round 3430 to 2 significant figures
= 3400
Round all of the numbers to four significantfigures
a. 84791 kg
b. 38.5432 g
c. 256.75 cm
d. 4.9356 m
e. 0.00054818 g
f. 136,758 kg
g. 308,659,000 mm
h. 2.0142 ml
Round all of the numbers to four significantfigures
a. 84791 kg = 84790 kg
b. 38.5432 g = 38.54 g
c. 256.75 cm = 256.8 cm
d. 4.9356 m = 4.936 m
e. 0.00054818 g = 0.00005482 g or 5.482 x 10-5g
f. 136,758 kg = 136,800 kg or 1.368 x 105 kg
g. 308,659,000 mm = 308,700,000mm or 3.087 x 108mm
h. 2.0142 ml = 2.014 ml
Round the following numbers asasked
White Boarding!!!!!!
Round 23.21004 to 3sig figs
23.2
Round 102,000 to 1 sigfig
100,000
Round 234,523.2 to 3sig figs
235,000
Round 910,230 to 4 sigfigs
910,200
Round 54.530 to 2 sigfigs
55
Round 46,000,000 to 1sig figs
50,000,000
Calculations with significant figures
1. For multiplication and division, the answers should be rounded off to the samenumber of significant figures in the measurement with the fewest significant figures
Ex. 3.01 x 2.0 = 6.02 6.0
Ex. 45 / 9.00 = 5.00 5.0
Example
I ride my bike to school. The distance is 4.1 miles. The other day it took25.7 minutes. What was my average speed, in miles per minute?
4.1 mi = 0.1595440793 mi
25.7 min min
4.1 mi = 0.16 mi
25.7 min min
Working with "Sig Figs"
Why did I convert 0.1595440793 mi/min to
0.16 mi/min and not something else?
Rules for working with significant figures:
Rounding
Sig figs in calculations
Addition and Subtraction
2.For addition and subtraction, the answers should be rounded off to the samenumber of decimal points as the measurement with the fewest decimalplaces.
Ex. 2.56 + 2.1 = 4.66 4.7
Ex. 34.232 + 22.4 = 56.632 56.6
Solve
4.00134 - 2.02 + 0.000071
4.00134 - 2.02 + 0.000071 = 1.981411 = 1.98
Solve
180,000 – 24,420 – 31,086
180,000 – 24,420 – 31,086 = 124,494 = 120,000
Precision decreases
Perform the following calculationsand round according to significantfigures or decimal places.
White Boarding!!!!!
40.50 + 2.3
42.8
3450 + 2
3450
1,205 + 3,100.4
4,305
10 - 9.9
0
5.5 + 3.7 + 2.97
12.2
4.5 - 5.00
-.5
7.77 / 2.3
3.4
3.890 / 121
.0321
120 x 0.0002
.02
0.00005 x 538
.03
Practice:
1)4.5 + 2.34 = _____________________
2)2) 4.5 – 5 = ________________________
3) 6.00 + 3.411 = _____________________
4) 3.4 x 2.32 = _______________________
5) 7.77 / 2.3 = ______________________
6) 3.890 / 121 = ______________________
7) 1200 x 23.4 = ______________________
8) 120 x 0.0002 = _____________________
9) 78.5 + 0.0021 + 0.0099 = ___________
10) (3.4 x 8.90) x (2.3 + 9.002) = _________
11) (2.31 x 103) / (3.1 x 102) = ___________
12) 0.0023 + 65 = __________________
Measurement Lab with Significant Figures
Objective: You will make many measurements in this experiment, and the goal is to record eachmeasurement with the correct number of significant figures, proper units, and uncertainties. You willalso make some simple calculations so make sure to use proper significant figures in the calculations.
- Digital measurement devices (balances and computer probes): Record all digits in the measurementgiven by the instrument, include the proper units, and record uncertainty (+/- the last shown digit).
- Analog measurement devices: Record all known digits, and estimate one digit “between the lines.” Besure to include units and uncertainty (+/- half of the smallest division on the scale).
- First Read through the lab and come up with a detailed data table to record important information on aseparate sheet of paper.
Length/Area: Measure the length and width of the piece of cardboard. Record the measurement incentimeters, paying close attention to recording the correct number of significant digits and make sure toinclude uncertainty.
Calculate the area of the paper, using the proper units (cm2) and significant figures.
Volume: Use graduated cylinders to measure volume
Obtain approximately 8 mL of water in a small beaker. Add the water to the 10-mL graduated cylinder andmeasure the volume. Record the volume, paying close attention to the significant figures. Be sure to include theproper units and uncertainty.
REPEAT FOR TWO MORE TRIALS (this means you will find the volume three times total)
Find the average of the three trials be sure to include the proper units and significant figures.
Mass: Use a balance to measure mass
Obtain a weighing boat record the mass of the boat OR zero the balance.
Find the mass of each of the objects in the PROCEDURE #3 bag individually paying close attention to the significantfigures. Be sure to include the proper units and uncertainty.
Find the total mass of all of the objects together. Make sure to use proper rules for addition in terms of significantfigures.
Temperature: Use a thermometer or temperature probe
Using a graduated cylinder measure approximately 150mL of distilled water into a 250 mL Erlenmeyer flask.
Heat the water to boiling using the hot plate.
Carefully record the temperature of the boiling water using the thermometer and the correct number ofsignificant figures. Be sure to record the proper units.
Assuming that the accepted value for water’s boiling point is 100.0°C, calculate the percent error.