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Chemistry and Measurement
Measuring Length: USE VIDEOS FOR DATA
1. What units are represented by the numbers marked on the meterstick?
What do the small lines marked on the meterstick represent? Complete the
centimeters (cm) in 1 meter (m). There are
millimeters (mm) in
1 meter (m).
millimeters (mm) in 1 centimeter (cm).
Width of little fingernail
Distance around wrist
Length of your shoe
Length of line
4. Number of
Your measurement (cm)
Other students’ values
How does your value of the line length compare to those of other students?
Questions and Problems
Q1 What digits in the measurements for the line by other students are the same as
yours and which are different?
skip this question
B. Measuring Volume: USE VIDEO FOR DATA
Volume of a liquid (include units for every measurement)
1. Volume (mL)
Volume of a solid by displacement
2. Initial volume of water
3. Volume of water and submerged solid
4. Volume of solid (3 − 2)
C. Measuring Mass: USE VIDEOS FOR DATA
Item 1. Mass
4. Number of Significant Figures
2. Irregular Solid
Questions and Problems
Q2 State the number of significant figures in each of the following measurements:
1 sig fig
6 sig fig
Q3 Indicate the estimated digit in each of the following measurements:
2 sig fig
estimated digit is
the last sig fig No.
4500. 4 sig fig
est. digit is
Use the links to watch the demonstrations
General Chemistry I Laboratory 1: Chemistry and Measurement.
• Identify metric units used in measurement, such as gram, meter, centimeter,
• Obtain a correct measurement using a meter stick, a balance, and a graduated
• State the correct number of significant figures in a measurement.
Time: 2 h
Tear out the report sheets and place them beside the
experimental procedures as you work.
Determine the markings on each measuring tool before you measure. Record all the
numbers for a measurement, including the estimated digit. Write a unit of
measurement after each measured number.
Significant figures, measured and exact numbers, metric
Scientists and allied health personnel carry out laboratory procedures, take
measurements, and report results accurately. The system of measurement used in
science, hospitals, and clinics is the metric system. The metric system is a decimal
system in which measurements of each type are related by factors of 10. You use a
decimal system when you change U.S. money. For example, 1 dime is the same as 10
cents or one cent is 1/10 of a dime. A dime and a cent are related by a factor of 10.
The metric system has one standard unit for each type of measurement. For
example, the standard metric unit of length is the meter, whereas the U.S. system of
measurement uses many units of length such as inch, foot, yard, and mile. Most of
the rest of the world uses the metric and the updated SI (International System of
Units) systems only. The most common units are listed in Table 1.1.
TABLE 1.1 Common Metric and SI Units of Measurement
Measurem Metric (Symbol) SI (Symbol) SI for this course
D = mass/volume
Temperatu degrees Celsius
1. tools to use
2. units of the tools
3. every numbers
4. rules for cal.
A unit is always included when reporting a measurement. For example, 5.0 m
indicates a quantity and unit in this measurement of length. Without the unit, we
would not know the units used to obtain the number 5.0. It could be 5.0 ft, 5.0 km, or
5.0 in. Thus, a unit is required to complete the measurement reported.
For larger and smaller measurements, prefixes are attached to the standard unit.
Some prefixes such as kilo are used for larger quantities; other prefixes such as milli
are used for smaller quantities. The most common prefixes are listed in Table 1.2.
TABLE 1.2 Common Prefixes in the Metric System
dm = 1/10 m
cm = 1/100 m
mm = 1/1000 m
A. Measuring Length
The standard unit of length in the metric system is the meter (m). Using an
appropriate prefix, you can indicate a length that is greater or less than a meter (see
Table 1.3). Kilometers are used in most countries for measuring the distance
between cities, whereas centimeters or millimeters are used for small lengths.
TABLE 1.3 Some Metric Units Used to Measure Length Length
1 km 1000 m or 103 m
1 dm 0.1 m (1/10 m) or 10−1 m
1 cm 0.01 m (1/100 m) or 10−2 m
1 mm 0.001 m (1/1000 m) or 10−3 m
A meterstick is divided into 100 cm, as seen in Figure 1.1. The smallest lines indicate
centimeters. That means that each measurement you make can be certain to the
centimeter. The final digit in a measurement is obtained by estimating between the
smallest marked lines. For example, the shorter line reaches the 44-cm mark and is
about halfway to 45 cm. We might report its length as 44.5 cm. The last digit (0.5) is
the estimated digit. If the line appears to end at a centimeter mark, then the
estimated digit is 0.0 cm. The longer line in Figure 1.1 appears to end right at the 67cm line, which is indicated by reporting its length as 67.0 cm (see Sample Problem
▲FIGURE 1.1 A meterstick divided into centimeters (cm)
SAMPLE PROBLEM 1.1
What is the estimated digit in each of the following measured masses?
a. beaker 42.18 g
b. pencil 11.6 g
a. hundredths place (0.08 g)
b. tenths place (0.6 g)
Chemistry and Measurement 4
B. Measuring Volume
The volume of a substance measures the space it occupies. In the metric system, the
unit for volume is the liter (L). Prefixes are used to express smaller volumes such
as deciliters (dL), centiliters (cL), or milliliters (mL). One cubic centimeter (cm3 or
cc) is equal to 1 mL. The terms mL and cc are used interchangeably (see Table 1.4).
TABLE 1.4 Some Metric Units Used to Measure Volume Unit of Volume
1 dL 0.1 L (1/10 L) or 10−1 L
1 cL 0.01 L (1/100) or 10−2 L
1 mL 0.001 L (1/1000 L) or 10−3 L
In the laboratory, the volume of a liquid can be measured in a graduated cylinder
(see Figure 1.2). Set the cylinder on a level surface and bring your eyes even with
the liquid level. Notice that the water level is not a straight line but curves
downward in the center. This curve, called a meniscus, is read at its lowest point
(center) to obtain the correct volume measurement for the liquid. Your eyes should
be aligned with the bottom of the meniscus in order to avoid error in making the
reading. In this graduated cylinder, the volume of the liquid is 42.0 mL.
▲FIGURE 1.2 Reading a volume of 42.0 mL in a graduated cylinder
On large cylinders, the lines may represent volumes of 2 mL, 5 mL, or 10 mL. On a
250-mL cylinder, the marked lines usually represent 5 mL. On a 1000-mL cylinder,
each line may be 10 mL. Then your precision on a measurement will be to the
milliliter or mL.
Volume of a Solid by Displacement
When an object is submerged in water, it displaces its own volume of water, causing
the water level to rise. The volume of the object is the difference in the water level
before and after the object is submerged (see Figure 1.3).
▲FIGURE 1.3 Using volume displacement to determine the volume of a solid
Chemistry and Measurement 5
C. Measuring Mass
The mass of an object indicates the amount of matter present in that object. In the
metric system, the unit of mass is the gram (g). A larger unit, the kilogram (kg), is
used for larger objects, for example, in measuring a patient’s weight in a hospital. A
smaller unit of mass, the milligram (mg), is often used in the laboratory (see Table
TABLE 1.5 Some Metric Units Used to Measure Mass Mass Value
1 kg 1000 g or 103 g
1 mg 1/1000 g (0.001 g) or 10−3 g
Measured and Exact Numbers
When we measure the length, volume, or mass of an object, the numbers we report
are called measured numbers. Suppose you stepped on a scale this morning and saw
that you weighed 145 lb. The scale is a measuring tool and your weight is a
measured number. Each time we use a measuring tool to determine a quantity, the
result is a measured number.
Exact numbers are obtained when we count objects. Suppose you counted 5 beakers
in your laboratory drawer. The number 5 is an exact number. You did not use a
measuring tool to obtain the number. Exact numbers are also found in the numbers
that define a relationship between two metric units or between two U.S. system
units. For example, the numbers in the following definitions are exact: 1 meter is
equal to 100 cm; 1 ft is equal to 12 in. (see Sample Problem 1.1).
SAMPLE PROBLEM 1.2
Describe each of the following as a measured or exact number:
a. 14 in. b. 14 pencils
c. 60 min in 1 h
d. 7.5 kg
a. measured b. exact (counted)
c. exact (definition) d. measured
In measured numbers, all the reported figures are called significant figures. The first
significant figure is the first nonzero digit. The last significant figure is always the
estimated digit. Zeros between other digits or to the right of the decimal point in a
decimal number are counted as significant figures. However, zeros to the left of
nonzero numbers are not significant; they are placeholders. Zeros are not significant
in large numbers with no decimal points; they are placeholders needed to express
the magnitude of the number.
When a number is written in scientific notation, all the figures in the coefficient are
significant. Examples of counting significant figures in measured numbers are in
Table 1.6 and Sample Problem 1.3.
Chemistry and Measurement 6
TABLE 1.6 Examples of Counting Significant Figures
0.80 m 2
50.2 L 3
25 000 ft
All nonzero digits are significant.
A zero following a decimal number is significant.
A zero between nonzero digits is significant.
Zeros to the left of nonzero numbers are not significant.
Placeholder zeros are not significant.
SAMPLE PROBLEM 1.3
State the number of significant figures in each of the following measured numbers:
b. 132.08 g
a. Three significant figures. The zeros after the decimal point are placeholder
zeros, but the zero following nonzero digits is significant.
b. Five significant figures. The zero between nonzero digits is significant.
When you use a meterstick, or read the volume in a graduated cylinder, the
measurement must be reported as precisely as possible. The number of significant
figures you can report depends on the lines marked on the measuring tool you use.
For example, on a 50-mL graduated cylinder, the small lines represent a 1-mL
volume. If the liquid level is between 21 mL and 22 mL, you know you can report 21
mL for certain. However, you can add one more digit (the last digit) to your reported
value by estimating between the 1-mL lines. For example, if the volume level was
halfway between the 21-mL and 22-mL lines, you would report the volume as 21.5
mL. If the volume level is exactly on the 21-mL line, you indicate this precision by
adding a significant zero to give a measured volume of 21.0 mL.
Chemistry and Measurement 7
A. Measuring Length
How to Use a Meter Stick
How to Measure Your Wrist (CONVERT to centimeters for practice 2.54 cm/inch)
How to Measure Parts of The Hand
Materials: Meterstick, string
1. Observe the marked lines on a meterstick. Identify the smallest lines on the
2. Use the meterstick to make the length measurements (cm) indicated on the
report sheet. String may be used to determine the distance around your wrist.
Include the estimated digit in each measurement.
3. Indicate the estimated digit in each measurement.
4. Indicate the number of significant figures in each measurement.
5. Measure the length of the line drawn on the report sheet including the
estimated value. Compare your value with those of two other students.
B. Measuring Volume
Measuring Volume in 10 mL Graduate Cylinder
Measuring Volume in 50 mL Graduate Cylinder
Measuring Volume in 100 mL Graduate Cylinder
Materials: Display of graduated cylinders with liquids, 10-mL, 50-mL, and 100-mL
(or larger) graduated cylinders, solid object, thread
Volume of a liquid
Read the volume of each of the liquids in the videos above of graduated
cylinders. Be as precise as you can. Be sure to estimate between the smallest
markings to obtain the estimated digit. Fill in the Table for Measuring a
Chemistry and Measurement 8
Volume of a solid by displacement
2. Obtain a graduated cylinder that will fit the solid object. Place water in the
graduated cylinder until it is about half full. Record the volume, in milliliters,
3. Tie a piece of thread around the solid object. Slowly lower the solid object
until it is completely submerged. Record the new volume of the water.
4. Calculate the volume, in milliliters, displaced by the solid.
C. Measuring Mass
Mass of an Eraser
Mass of Irregular Object
Materials: Balance, objects to weigh (eraser, and irregular object)
The videos will show you how to use a laboratory balance. Be sure the reading
is 0.00 when the balance pan is empty.
1. Separately place each object on the balance pan and record its mass.
2. Obtain the mass of the object from your instructor and compare to your
3. Determine the correct number of significant figures for each mass obtained.
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