Significant Digits in Measurement of Matter
PRELAB DISCUSSION
Measurements are an important part of science; they are all a part of quantifying matter
so that we can have a better understanding of the world. It is very important to be able to
describe matter in a quantitative, or measurable, sense.
No measured quantity can ever be exact; there will always be some uncertainty
associated with it. The degree of certainty in a measurement is reflected in the number of
significant digits contained in it. The significant digits in a measurement contain all of
the certain digits – those of which we can be sure- and one uncertain digit. Just where the
uncertainty lies depends on the instrument being used. Measuring instruments that have
smaller divisions (Ex: mm instead of cm) allow greater certainty in measurement.
PURPOSE
To familiarize yourself with common laboratory measuring instruments for length, mass,
and volume, and to learn about uncertainties in measurement. To express measurements
and calculations using the proper number of significant digits. To indicate the accuracy
in measurements by calculating percent error.
MATERIALS
balance
calculator
graduated cylinder, 10mL
water
metric ruler
pennies
test tube
PROCEDURE
1. Measure the thickness of one penny, being certain to include one estimated
number in your measurement. (Record: 1a)
2. Repeat step 1 for stacks of pennies containing 4, 7, and 10 pennies; be sure to
obtain as many significant digits as are allowed for your ruler. (Record: 1b-d) As
you measure the pennies, note if there is any observable variation in the thickness
of each.
3. Carefully measure the length and width of the cover of your chemistry book in
units of centimeters. The first time, measure it as if there were no millimeter
markings on the ruler; that is estimate the tenths place in the measurement.
(Record: 2 a-b) The second time, use the millimeter markings to estimate the
hundredths place. (Record: 2 c-d)
4. Using the lab balance, find the individual masses of 5 of your pennies. Select
pennies that have a variety of dates- some newer and some older. Use significant
digits properly in your recorded values. (Record: 3) Do you notice any difference
in the mass of a penny relative to the year it was minted?
5. Fill a test tube to the brim with water and carefully transfer all of it to your
graduated cylinder. Using just your eye, measure the volume of water that the test
tube contained. Be sure to include one estimated number in your measurement.
(Record: 4a) Repeat this measurement of the volume of the same test tube two
more times, being careful to fill the test tube to the brim each time. (Record: 4 bc)
DATA
1. Number of pennies in a stack
1
Measured thickness
(a)________ cm
(b)_________ cm
7
10
(c)________ cm
(d)_________ cm
Number of pennies in a stack
Measured thickness
2.
nearest tenth
4
nearest hundredth
Length of book
(a)_________ cm
(c)__________ cm
Width of book
(b)_________ cm
(d)__________ cm
3. Mass of penny
Year of penny
________g ________g ________g ________g ________g
________
_________ _________ ________ _________
4. Volume of water (a) _______mL (b) _________ mL
(c) ________mL
CONCLUSION AND QUESTIONS.
1. Calculate the average thickness of one penny for each set of pennies, using
significant digits properly.
Number of pennies
Average thickness
1
_______cm
4
________cm
7
10
________cm
________cm
2. Which of these numbers is the most representative for the average thickness of a
penny? Explain.
3. Assume the true thickness of a penny is 1.4mm. Calculate % error using your most
accurate average.
3. Calculate the area of the cover of your chemistry book (length x width) ; then
calculate its perimeter (length + length + width + width). Record both the
unrounded value and the value with the proper number of significant digits.
Unrounded
Using Significant Digits
Area, using 2a-b
_______ cm2
_________ cm2
Area, using 2c-d
_______cm2
_________ cm2
Perimeter, using 2a-b
_______ cm
_________ cm
Perimeter, using 2c-d
_______ cm
_________ cm
4. Which set of calculated quantities is closer to the actual, exact area and perimeterthose using 2a and 2b, or those using 2c and 2d? Explain.
5. In what decimal place was there uncertainty in the masses of the pennies?
6. Did you notice any age-related mass difference in the pennies? If so, what was it?
7. Calculate the average mass of a penny, expressing it with the proper number of
significant digits. Is it possible for your average to be significantly different from
that obtained by another group in your class? Explain.
Average mass of a penny________ g
8. Calculate the average volume of water contained in your test tube.
Average volume ____________ mL
9. In what decimal place is the uncertainty (precision) in your measurement of the
water?
10. Do you think the average of three trials gives a more reliable (more accurate)
value for the volume of the test tube than a single measurement? Why or why not?