NAME:___________________________________
DATE:_____________________
PERIOD:_____
#:_____
Significant Figures & Measurement Lab
Purpose
At the core of all science is the ability to take accurate and precise measurements and to do
calculations. Central to these concepts are significant figures, because they help tell us how
accurate measurements are. In this lab, you will gain experience with all of these concepts.
Background
Significant figures are nothing more than the amount of digits we get from a measurement. The
better a measurement is, the more significant figures you will have. For example, if you
measure a sample on a balance and the balance reads 2.543 g, then there are 4 significant
figures. If you measure the same sample on a more sensitive balance, it may read 2.5432 g. The
second measurement has 5 significant figures, and reflects a better measurement. This also
means that for numbers that you don’t measure, such as conversion factors, there are no
significant figures.
An important note to make is that the very last digit in a measurement is always the least
certain. Two people reading the same length on a ruler may see 1.24 cm vs. 1.25 cm. All three
numbers are significant figures, but the last number has a bit of uncertainty because it is
estimated. Both values are correct because it is expected that the last number is the uncertain
one.
To measure with significant figures, you count ALL digits. Each one is considered significant. For
example, a ruler that reads 1.36 cm has 3 significant figures. A beaker with 12.52 mL of liquid
has 4 significant figures. Scientific equipment has markings that let you read its measurement
to a certain number of significant figures. The last value in your reading will ALWAYS be an
estimate between the markings. This is why no two people will necessarily have the same exact
number.
Ruler Example:
Here we see a ruler with markings for every centimeter, but none in between. The
measurement between 6 and 7 looks to be a little before the half‐way point. Acceptable
answers for this measure of distance would be anywhere from 6.2‐6.4 cm.
cm
Volume Example:
When you read volumes in glassware, you always read the
bottom of the meniscus so that it is at your eye level.
The meniscus here is right around the 11.5 mL marking.
Possible answers would be 11.49‐11.52 mL.
You read a thermometer in the same way.
Significant Figures & Measurement Lab
Calculating with Significant Figures
In addition and subtraction, pick the number with the fewest decimal places. Use that same
number of decimal places in your final answer.
Examples:
12.0 + 12.13 = 24.1
0.02‐0.0032=0.02
In multiplication and division, you need to determine which numbers are indeed significant.
In your final answer, use as many significant figures as the number with the fewest significant
digits.
Examples:
0.00352 X 125 = 0.440
143/0.02010 = 7110 OR 7.11 X 103
Procedure – Part A
There are stations set up around the lab that you will visit. Read the equipment at each station
and record your values on the data sheet. You can start with any station. Record
measurements with the proper number of significant figures.
a. Station 1: Reading Burets
Burets are long pieces of glass with calibrated markings on the side. They are marked
backwards, where the 0‐mL mark is at the top, and the 50‐mL mark is at the bottom. These
are used to measure the amount of liquid that is delivered by subtracting numbers. Read
and record the volumes on the two burets.
b. Station 2: Reading Erlenmeyer Flasks
Erlenmeyer flasks are pieces of glassware that are tapered up at the top and graduated
along the sides. These are so large that a meniscus can’t usually be read. These are not used
to measure exact volumes, but more estimates of large volumes. Read and record the
volumes on the Erlenmeyer flasks.
c. Station 3: Graduated Cylinders
Graduated cylinders are used to measure more exact volumes of liquid. They are thin glass
tubes with markings up the side, similar to a buret, except they start at 0‐mL and go up.
These will show a meniscus, so be careful when you are reading them. Read and record the
volumes on the graduated cylinders.
d. Station 4: Beakers
Beakers are cylindrical glass containers which are commonly used for crude measurements
and mixing chemicals. Beakers come in many sizes, from less than 10‐mL to over several
liters! Read and record the volumes on the beakers.
e. Station 5: Thermometers
In science, we measure all of our chemicals based off the Celsius (˚C) scale. Read and record
the temperatures of the beakers of water set out.
Significant Figures & Measurement Lab
Procedure – Part B
For this activity, you will be measuring the geometric shapes on the bottom of this page using
three different rulers. Ruler 1 only has markings every 10 centimeters. Ruler 2 has markings
every centimeter and ruler 3 is a standard ruler with 1 millimeter markings. Record
measurements with the proper number of significant figures.
1.
2.
3.
4.
Measure the length and width of the rectangle with Ruler 1.
Measure the base, height, and all three sides of the triangle with Ruler 1.
Measure the radius and diameter of the circle with Ruler 1.
Repeat steps 1-3 with Ruler 2 and then Ruler 3.
Significant Figures & Measurement Lab
Procedure – Part C
In science, we must often make use of one set of measurements to indirectly measure other
quantities, because they are difficult to directly measure. For example, we do not have the
equipment in our lab to directly measure the thickness of a piece of aluminum foil or the
diameter of a piece of copper wire. However, we can determine exact volumes of these
materials by using density values and the dimensions of the samples that we can measure. You
will need to determine what data to collect to determine the unknown values.
1. Given a square of aluminum foil, determine the thickness (height) of the sample.
Outline your procedure in the space below. NOTE: Volume of the foil is length x width x
height and the density of aluminum is 2.70 g/cm3.
2. Given a piece of copper wire, determine the diameter (2r) of the wire. Outline your
procedure in the space below. NOTE: Volume of the wire is πr2h and the density of
copper is 8.96 g/cm3.
NAME:___________________________________
DATE:_____________________
PERIOD:_____
#:_____
Significant Figures & Measurement Lab
Data – Part A
Reading 1
Reading 2
Station 1: Burets
Station 2: Erlenmeyer Flasks
Station 3: Graduated Cylinders
Station 4: Beakers
Station 5: Thermometers
Data – Part B
RECTANGLE
Ruler Ruler Ruler
1
2
3
Ruler
1
TRIANGLE
Ruler Ruler
2
3
Ruler
1
CIRCLE
Ruler Ruler
2
3
Units
Length
Base
Radius
Width
Height
Diameter
Side A
Side B
Side C
Data – Part C
1. Report all data collected for the aluminum foil. Express answers with proper number of
significant figures. DO NOT PERFORM ANY CALCULATIONS YET.
2. Report all data collected for the copper wire. Express answers with proper number of
significant figures. DO NOT PERFORM ANY CALCULATIONS YET.
Significant Figures & Measurement Lab
Calculations & Conclusions – Part A
1. For the numbers below, state how many significant figures there are:
a. 0258 _________
b. 1.024 _________
c. 0.2600 _________
d. 1345.1 _________
e. 1000.1 _________
2. Calculate the answers to the following operations using the correct number of
significant figures.
a. 1.2 + 0.13 =_________
b. 1.2 x 0.13 =_________
c. 485.369 ÷ 0.124 =_________
d. 0.0012 - 0.0008 =_________
e. [1.265 + 1.02] x 82 =_________
3. For station 1, add together the buret volumes.
4. Multiply your buret volumes and subtract them from 100.1 mL.
5. For station 2, subtract volume “B” from volume “A”.
6. For station 3, multiply the volumes in the graduated cylinders.
7. Subtract “A” from “B” in the graduated cylinders, then add 0.223 mL.
Significant Figures & Measurement Lab
8. For station 4, subtract volume “A” from volume “B”.
9. For station 5, divide temperature “A” by “B”.
10. Do the following calculation:
Calculations – Part B
Show all work for the calculations below. Be sure to express answers with proper number of
significant figures.
1. Calculate the perimeter of the rectangle:
a. Ruler 1:
b. Ruler 2:
c. Ruler 3:
2. Calculate the area of the rectangle (LxW):
a. Ruler 1:
b. Ruler 2:
c. Ruler 3:
3. Calculate the perimeter of the triangle:
a. Ruler 1:
b. Ruler 2:
c. Ruler 3:
Significant Figures & Measurement Lab
4. Calculate the area of the triangle (½bh):
a. Ruler 1:
b. Ruler 2:
c. Ruler 3:
5. Calculate the circumference of the circle (2πr):
a. Ruler 1:
b. Ruler 2:
c. Ruler 3:
6. Calculate the area of the circle (πr2):
a. Ruler 1:
b. Ruler 2:
c. Ruler 3:
Conclusions – Part B
1. To what precision (decimal place) did you report each of the measurements made with
Ruler 1? Explain why?
2. Was the number of significant figures for each of your measurements with Ruler 2
constant? Explain.
3. Explain how you determined how many significant figures to include in the results of
each of the calculations done with the measurements from Ruler 3.
Significant Figures & Measurement Lab
Calculations – Part C
1. Show all calculations performed to determine the thickness of the foil. Express all
answers with the proper number of significant figures.
2. Show all calculations performed to determine the diameter of the wire. Express all
answers with the proper number of significant figures.