Activity No.

1 Part 1
SIGNIFICANT FIGURES

Objectives
From this activity, the student should be able to:
1. Familiarize the rules in determining the numbers of significant figures in a given
measurement, and
2. Use the rules of determining the numbers of significant figures in performing the fundamental
operations and solving word problems.

Unlike counting, measurement is never exact. You can count exactly ten people in a room. If you
ask each of these people to measure the length of the room to the nearest 0.01 m, however, the values
they determine are likely to differ slightly. Table 1 presents such a set of measurements.
Note that all ten students agree on the first three digits of the measurement; differences occur in the
fourth digit. Which values are correct? Actually, all are accurate within the accepted range of uncertainty
for this physical measurement. The accuracy of the measurement depends on the type of measuring
instrument and the skill and care of the person making the measurement. Measured values are usually
recorded with the last digit regarded as uncertain.
The data in Table 1 allow us to state that the length of the room is between 14.1 m and 14.2 m, but
we are not sure of the fourth digit. The measurements in the table have four significant figures, which
mean that the first three are known with confidence and the fourth conveys an approximate value.
Significant figures include digits known with certainty plus one uncertain digit.

Table 1. Set of measurements of the length of a room.

Student Length (m) Student Length(m)
1 14.14 6 14.14
2 14.15 7 14.17
3 14.17 8 14.17
4 14.14 9 14.16
5 14.16 10 14.17

In any properly reported measurement, all nonzero digits are significant. The zero presents a
problem, however, it can be used in two ways: to position the decimal point or to indicate a measured
value. For zeros, follow these rules:

1. A zero between two other digits is always significant.

Ex. 1107 – contains four significant figures
2. Zeros to the left of all nonzero digits are not significant.
Ex. 0.000163 – contains three significant figures
3. Zeros that are both to the right of nonzero digits are significant.
Ex. 802.760 – contains six significant figures
4. Zeros in numbers such as 40, 000 (that is, zeros to the right of all nonzero digits in a number that is
written without a decimal point) may or may not be significant. Without more information, we simply
do not know whether 40,000 was measured to the nearest unit of ten or hundred or thousand or ten
thousand. To avoid this confusion, scientists use Scientific Notation (or exponential
notation).
Ex. 40,000 = 4 x 104 (one significant figure) or
= 4.0 x 104 (two significant figures) or
= 4.0000 x 104 (five significant figures)
Scientific Notation
Scientific notation is writing a number as the product of a number between 1 and 9 multiplied by 10
raised to some power.
• Used to express very large numbers or very small numbers as powers of 10.
• Write 45,000,000 in scientific notation
– Move the decimal point (leftward) so that it is located after the first nonzero digit (5.94)
– Indicate the power of 10 needed for the move. (107)
= 4.50×107
• Exponent is equal to the number of places the decimal point is moved.
• Sign on exponent indicates the direction the decimal was moved
– Moved right → negative exponent
– Moved left → positive exponent
• Write 0.000509 in scientific notation
– Move the decimal point (rightward) so that it is located after the first nonzero digit
(3.50)
– Indicate the power of 10 needed for the move. (10-4)
• 5.09×10-4
ROUNDING OFF NONSIGNIFICANT DIGITS
Rules in Rounding Off
If the leftmost digit to be removed is less than 5, the preceeding number is left unchanged. If it is 5 or
greater, the preceding number is inceased by 1.

How do we eliminate nonsignificant digits?

ROUND DOWN If first nonsignificant digit < 5, just drop ALL nonsignificant digits
ROUND UP If first nonsignificant digit ≥ 5, raise the last sig digit by 1 then drop ALL nonsignificant
digits
Examples:
❖ 9.239899 rounded to 2 significant figures is 9.2
❖ 0.033462 round to 3 significant figures is 0.0335

Significant Figures in Calculations

In Addition or Subtraction:
− The result should contain no more digits to the right of the decimal point than the quantity that
has the least digits to the right of the decimal point.
− Align the quantities to be added to the right of the decimal point and then perform the
operation, assuming blank spaces are zeros.
− Determine the correct number of digits after the decimal point in the answer and round off to
this number.
− In rounding off, you should increase the last significant figure by one if the following digit is
five through nine.

Ex. Add the following numbers: 49.146, 72.13, 5.9432

Align the numbers on the decimal point and carry out the addition.
 49.146 The quantity with the least digits after the decimal point is 72.13.The
72.13 answer should have only two digits after the decimal point. Since
+ 5.9432 the third digit after the decimal point is 9, the second digit after the
127.2192 decimal point should be rounded up to 2.
Correct answer: 127.22

In Multiplication or Division:
− The number of significant figures in the final answer should be the same to that of the factor
with the least number of significant figures
− In the operation, the position of the decimal point makes no difference.

Ex. Multiply 10.4 by 3.1416

10.4 x 3.1416 = 32.67264 →32.7
The final answer is rounded off to three significant figures because the term with the least
number of significant figures is 10.4 with three SF.

Exact values
• Some quantities are not measured but defined.
− A kilometer is defined as 1000 meters: 1 km = 1000 m.
− Similarly, 1 foot can be defined as 12 inches: 1 ft = 12 in.
• The “1 km” should not be regarded as containing one significant figure nor should “12 in.” be
considered to have two significant figures. In fact, these values can be considered to have an
infinite number of significant figures (1.000 000 000 000 000 0…) or, more correctly, to be exact.
• Such defined values are frequently used as conversion factors in problems. When you are
determining the number of significant figures for the answer to a problem, you should
ignore such exact values.
• Use only the measured quantities in the problem to determine the number of significant figures in
the answer
 Activity No. 1 (Dry Lab)
MEASUREMENTS AND SIGNIFICANT FIGURES

NAME: ___________________________________________ SCORE: _________/38

INSTRUCTOR: __________________________________ DATE: ____________

A. How many significant figures are there in each of the following numbers? 1 pt each.

_________________ 1. 100 _________________ 6. 3.678

_________________ 2. 2.001 x 1013 _________________ 7. 0.0100130

_________________ 3. 7.330 _________________ 8. 5.100 x 10-4

_________________ 4. 400.01 _________________ 9. 2360305

_________________ 5. 14780.1 _________________ 10. 23.004 x 10-5

B. Perform the indicated operation and express your answer with the correct number of significant
figures. (2 pts each)

1. (18 x 165 x 5.3) ÷ (3.3 x 6.0 x 4.7) = ______________________________

2. 7.87 ÷ (26.1 - 8.24) = ______________________________

3. (2.42 + 15.7) ÷ 2.9 = ______________________________

4. 35632 + 7.62 + 1.3 = ______________________________

5. (325 x 40.8) + (627 – 375) = ______________________________

C. Answer as directed. Show Solutions.

1. Express the following numbers in scientific notation with 3 significant figures. (1 pt. each)
a. 65310 ______________________________
b. 0.000630 ______________________________
c. 856500 ______________________________
d. 16000 ______________________________
 e. 0.001016 ______________________________

2. The diameter of the cylinder is 15.2 cm and the height is 165.4 cm. Calculate the volume of water
needed to fully filled this cylinder. Show your complete solution and answer with the correct number of
significant figures. (3 pts.)

3. Calculate the average mass of the three samples that have the masses of 10.25 g, 5.5654 g, and
105.4 g. Show your answer with the correct number of significant figures. (3 pts.)

4. What is the mass of a rectangular piece of copper with dimensions of 142.6 cm x 21.4 cm x 9.5 cm?
The density of copper is 8.92 g/cm3? (3 pts.)

5. The World Meteorological Organization has determined that the world's former record high
temperature 136.4°F (at Al Aziziyah, Libya on September 13, 1922) was miscalculated by about 12.6°F.
What is the correct temperature, in °C, taking into consideration the 12.6°F mistake? (4 pts)
 Activity No. 1 Part 2
Measurements and Conversion of Units

Objectives
From this activity, the student should be able to:
1. Know the difference of counting numbers and measurements,
2. Know the difference of precision and accuracy,
3. Perform dimensional analysis/factor label method, and
4. Answer word problems involving derived units.

Measurement: Units and Handling Numbers

➢ Many properties of matter are quantitative: associated with numbers.
➢ A measured quantity must have BOTH a number and a unit.

Two types of numbers:

• Exact numbers (known as counting or defined).
• Inexact numbers (derived from measurement).

All measurements have some degree of uncertainty or error associated with them.
• Precision: how close a set of measurements are to each other.
• Accuracy: how close a measurement is to the “true value”.

good accuracy but poor precision

poor precision & poor accuracy

Metric System

The metric system or International System (SI) is a decimal system of units that uses factors
of 10 to express larger or smaller numbers of these units.

Length and Mass

➢ SI base unit of length = meter (1 m = 1.0936 yards).
➢ SI base unit of mass (not weight) = kilogram (1 kg = 2.2 pounds).

• Mass is a measure of the amount of material in an object.

• Weight is a force that gravity exerts on an object. Weight = mass x gravity
The Seven SI Base Units
Physical Quantity Name of Unit Abbreviation
Mass Kilogram Kg
Length Meter m
Time Second s (sec)
Temperature Kelvin K
Amount od substance Mole mol
Electric current Ampere A
Luminous intensity Candela cd

Commonly Used Prefixes in the Metric System

Temperature
➢ Celsius scale: Water freezes at 0 oC and boils at 100 oC (sea level). 9
➢ Kelvin scale (SI Unit): based on the properties of gases. F = C + 32
5
5
• Water freezes at 273.15 K (32 oF) and boils at 373.15 K (212 oF ) at sea level. C = (F − 32)
9
• Zero is lowest possible temperature (absolute zero). (0 K = –273.15 C)
o C = K − 273.15

➢ Fahrenheit (not commonly used in science): K = C + 273.15

Derived SI Units
➢ These are formed from the 7 base units.

Example: Velocity is distance traveled per unit time, so units of velocity are units of distance (m)
divided by units of time (s): m/s.

Volume
➢ S. I. Unit of volume = (units of length)3 = m3.
This unit is unrealistically large, so we use more reasonable units:

• cm3 (also known as mL (milliliter) or cc (cubic centimeters))

• dm3 (also known as liters, L).
➢ Important: The liter is not an SI unit.
Density
➢ Used to characterize substances. S. I. unit = kg/m3. (1 g/cm3 or g/mL = 1000 kg/m3)
➢ Density is defined as mass divided by volume.
➢ Units: g/cm3 or g/mL (for solids and liquids); g/L (often used for gases).
➢ Originally based on mass (the density was defined as the mass of 1.00 g of pure water).

Problem Solving: Dimensional Analysis/Factor Label Method

➢ Dimensional analysis is a method of solving problems utilizing a knowledge of units.
➢ Given units can be multiplied and divided to give the desired units.
➢ Conversion factors are used to manipulate units:
Desired unit = given unit x (conversion factor).
➢ The conversion factors are simple ratios:

Conversion factor = (desired unit) / (given unit).

Using Two or More Conversion Factors

➢ We often need to use more than one conversion factor in order to complete a problem.
➢ When identical units are found in the numerator and denominator of a conversion, they will
cancel. The final answer MUST have the correct units.
For example:
Suppose that we want to convert length in meters to length in inches. We could do this
conversion with the following conversion factors:
1 meter = 100 centimeters and 1 inch = 2.54 centimeters

The calculation would involve both conversion factors; the units of the final answer will be inches:
(# meters) (100 centimeters / 1 meter) (1 inch / 2.54 centimeters) = # inches

STEPS IN SOLVING PROBLEMS

1. Write the units for the answer.
2. Determine what information to start with.
3. Arrange all other unit factors—showing them as fractions—with correct units in the numerator
and denominator, so all units cancel except for the units needed for the final answer.
4. Check for correct units and number of sig figs in the final answer.
 Activity No. 2 (Dry Lab)
MEASUREMENTS AND COVERSION OF UNITS

NAME: ___________________________________________ SCORE: _________

INSTRUCTOR: __________________________________ DATE: ____________

I. Make the following unit conversions. Show all necessary solutions and report your answers with
correct number of significant figures. (2 pts. each)

(a) 96.4 mL to L (f) 62 g to ng

(b) 45.7 kg to g (g) 33.61 m3 to L
(c) 21.64 dm3 to mL (h) 43.7 L to gal
(d) 63.7 mg to g (i) 1.1 mi to mm
(e) 2.73 gal to L (j) 34.9 mm to km

II. Problem Solving. Show all necessary solutions and report your answers with correct number of
significant figures. (3 pts. each)

1. Thermometers are often filled with liquid mercury, which melts at 234 K. What is the melting point
of Hg in °F?

2. Normal body temperature is 98.6°F. What is that temperature in °C?

3. The volume of a rock weighing 1.075 kg is 334.5 mL. What is the density of the rock in g/mL?
Express it to three significant figures.

4. The density of titanium is 4.54 g/mL. What is the volume, in milliliters, of 163 g of titanium?

5. A rectangular aquarium has dimensions of 145.3 cm x 46.7 cm x 25.2 cm. Determine the volume
of this aquarium in Liters.

6. Convert 45.0 km/hr to m/s.

 Activity 1 Part 3

MEASUREMENTS

Chemistry is a science that should be approached through experimentation and observation. The
Chemistry Laboratory is a place where one learns Chemistry by observing what substances do under fixed
conditions and what happens when these conditions are changed. Many of the observations needed are of
quantitative measurement, i.e., the magnitude of some properties like temperature, pressure, size, volume,
etc. is measured and expressed as a number using some instruments. To make such measurements, a
system of units is needed to express the data.
The precision of a measurement is the agreement of values obtained under the same conditions. The
accuracy of the measurement is the degree of agreement between the true value and the measured value.
Any measurement must be estimated to convey just the right degree of accuracy and precision – no more
and no less – as warranted by the equipment and the conditions of the experiment.
It is therefore appropriate that at the beginning of the course, attention must be given to the problems
of measurements, the units in which they should be expressed and their accuracy.

OBJECTIVES:
To be able to use the balance properly and determine the precision of selected apparatus.
To know how to perform volume and density measurements.
To determine the correct number of significant figures.
APPARATUS:
Tap Loading balance ruler thumb-sized stone
250-mL beaker regular solid
10, 50, 100-mL graduated cylinders small test tube
PROCEDURE:

A. Determination of Precision
Determine the precision of a 10-, 50-, and 100-mL graduated cylinders, thermometer, and
beam balance using the following steps:
1. Determine first the smallest calibration, SC, of the apparatus.
𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒃𝒆𝒕𝒘𝒆𝒆𝒏 𝒂𝒏𝒚 𝒕𝒘𝒐 𝒔𝒖𝒄𝒄𝒆𝒆𝒅𝒊𝒏𝒈 𝒔𝒄𝒂𝒍𝒆𝒔
𝑺𝑪 =
𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒊𝒗𝒊𝒔𝒊𝒐𝒏𝒔
Example: The smallest calibration of a certain weighing instrument is
(𝟏−𝟎)𝒈 (𝟐−𝟏)𝒈
𝑺𝑪 = = 𝟎. 𝟏𝒈 or 𝑺𝑪 = = 𝟎. 𝟏𝒈
𝟏𝟎 𝟏𝟎
2. The precision, P is computed using the formula:
𝑺𝑪
𝑷=±
𝟐

𝟎.𝟏𝒈
Example: 𝑷 = ± = ±𝟎. 𝟎𝟓𝒈
𝟐

Note: Incorporate the precision of each measuring device on the reported corresponding measured value.
Show calculation(s) to your instructor before proceeding to section B.

1
B. Determination of Mass
Rough weighing is made on a beam balance. Take the masses of 250-mL beaker and a 10-mL
graduated cylinder. Record the data considering the precision of the balance.

C. Determination of Volume
Fill a 100-mL graduated cylinder with water to its brim. Measure the volume of the
uncalibrated portion of the 100-mL graduated by pouring the water into a 50-mL graduated cylinder.
Also, measure the volume of a small test tube by filling it with water and transfer the water into a 10-
mL graduated cylinder.

D. Determination of Density

1. Density of a Liquid
Measure 15 mL of water using the 50-mL graduated cylinder. Take the mass of this cylinder with
the water. Calculate the density. Report it to the proper number of significant figures.

2. Density of a Regular Solid

Obtain a solid sample with a regular shape. Weigh the sample and record. Measure its dimensions.
Calculate the volume. Calculate its density.

3. Density of a Solid Sample by Water Displacement

Obtain a thumb-sized stone. Clean, weigh and record. Pour approximately 50mL of water in a 100-
mL graduated cylinder. Read and record this volume. Carefully place the stone into the water and
note the new volume. Calculate the volume of the sample. Report it to the proper number of
significant figures. Calculate the density.

2
 Activity 1 Part 3
MEASUREMENTS

Section: ________ Date Performed: _________

Name: ____________________________________ Score: _____
Rating: _________

DATA AND RESULTS

A. Determination of Precision

Apparatus Smallest Calibration, Precision, P

SC

10-mL graduated cylinder

50-mLgraduated cylinder
100-mL graduated cylinder
Ruler

B. Determination of Mass

Apparatus Mass (g)

250-mL beaker
10-mL graduated cylinder

C. Determination of Volume

Apparatus Volume (mL)

Uncalibrated portion of 100-mL graduated cylinder

Small test tube

D. Determination of Density
1. Density of a Liquid

a. Mass of empty 50-mL graduated cylinder, g

b. Mass of 50-mL graduated cylinder with water , g

3
 c. Mass of water (b-a), g
d. Volume of water, mL
e. Density of water at room temperature, g/mL
Show your calculation below for the density of water.(2 pts)

2. Density of a Regular Solid

Shape of sample: ________________________

Mass of sample, g
Length (cm)
Width (cm)
Dimension (if applicable) Height (cm)
Radius (cm)
Volume of the sample, cm3
Density of the solid, g/cm3
Calculate the density of the solid sample. Show your solution.(2 pts)

3. Density of a Solid by Water Displacement

a. Mass of the sample, g

b. Volume of water in the cylinder, mL
c. Volume of water + sample, mL
d. Volume of sample(c-b), mL
e. Density of the solid sample, g/mL
Calculate the density of the solid sample. Show your solution. (2 pts)