Updated version of Ch.1, Lecture B.

1. 1/11/13
CHM 101
Chapter 1: Matter & Measurement
Part B

2. Scientific Notation
Scientific notation is used to write very large or very small numbers.
A number in scientific notation contains a coefficient and a power of 10.
coefficient power of ten coefficient power of ten
1.5 x 102 7.35 x 10-4
To write a number in scientific notation, the decimal point is moved so it will lie after
the first digit.
All significant figures are written.
52 000. = 5.2000 x 10 4 0.00378 = 3.78 x 10-3
4 spaces left 3 spaces right (use negative exponent)
(use positive exponent)
See Section 1.6 in your text for a detailed treatment of scientific notation (ASK FOR HELP!)

3. Units of Measurement
You MUST know the prefixes below and be able to use them
as conversion factors.
Used to
represent
large
quantities
Used to
represent
small
quantities

4. Equalities
An equality states the same measurement in two different units, or in the same unit
with two different prefixes.
1 km = 1 x 103 m 1 cm = 1 x 10-2 1 mg = 1 x 10-3 g
1 m = 1 x 10-3 km m
1 x 103 mg = 1 g
1 m = 100 cm
1000 m = 1 km 1000 mg = 1 g
Equalities are also written for relationships between units of the metric
system, U.S. units, or between metric and U.S. units.
1 in. = 2.54 cm 454 g = 1 lb

5. Conversion Factors
A conversion factor is a fraction obtained from an equality.
Equality: 1 in. = 2.54 cm
The conversion factor is written as a ratio with a numerator and denominator.
It can be inverted to give two conversion factors for every equality.
1 in. 2.54 cm
or
2.54 cm 1 in.
Equality: 1 m = 1 x 106 mm
6
1m 1 × 10 μ m
6 or
1 × 10 μ m 1m

6. Factor-Label Method for Conversions
How many minutes are 2.5 hours?
Given unit = 2.5 hr
Needed unit = min
Unit Plan = hr min
Setup problem to cancel hours (hr).
Given Conversion Needed
unit factor unit
2.5 hr x 60 min = 150 min (2 SF)
1 hr
**Always write out the conversion factor with units. Cross through
the units that cancel and make sure you end with the desired unit.

7. Factor-Label Method for Conversions
How many minutes are 2.5 hours?
Given unit = 2.5 hr
Needed unit = min
Unit Plan = hr min
Setup problem to cancel hours (hr).
Given Conversion Needed
unit factor unit
2.5 hr x 60 min = 150 min (2 SF)
1 hr
**Always write out the conversion factor with units. Cross through
the units that cancel and make sure you end with the desired unit.

8. Units & Conversion Factors
The diameter of an average sodium atom is 186 nm. What is the diameter in cm?
In inches?
A man weighs 83.95 kg. What is his weight in pounds?
Do you know how to enter scientific notation on your calculator?

9. Density
Density – physical property, ratio of the mass of a substance to its
volume.
mass
density =
volume
Common units of density
include g/mL, kg/L, etc.
Ice floats in water because the
density of ice is less than the
density of water.
Aluminum sinks because its
density is greater than the
density of water.

10. Density
The mass and volume of a substance can be used to calculate
density, which can then be used to identify the substance.
Answer the following questions without doing calculations:
1. Which has a larger mass: 1.0 mL gasoline or 1.0 mL water?
2. Which has a greater volume: 1 g bone or 1 g table sugar?

11. Density
Density can be written as an equality and used as a conversion factor.
For a substance with a density of 3.8 g/mL, the equality is
3.8 g = 1 mL
From this equality, two conversion factors can be written for density.
3.8 g or 1 mL
1 mL 3.8 g
*Calculate the volume of a 25.7 g sample of iron. Iron has a density of 7.86 g/mL.
*Calculate the mass 150. mL of ethanol (d = 0.789 g/mL).

12. Density
Specific Gravity – ratio of the density of a substance to the density of water.
density of a substance (g/mL)
specific gravity =
density of water (g/mL)
Specific gravity has no units.
*The specific gravity of a urine sample is measured to be 1.020. What volume of this
urine sample would have a mass of 35 g?

13. Temperature
Temperature is a measure of how hot or cold an object is compared to
another object. Common temperature scales include Celsius,
Fahrenheit, and Kelvin.
TF  9 (TC )  32

5
TC  5
9
T F
 32


T K  TC  273 . 15
You MUST be able to convert
between the 3 temperature
scales: Celsius, Fahrenheit, and
Kelvin.

14. Record the temperatures on the thermometers
below as accurately as possible.
28°C 28°C
27°C 27°C
26°C 26°C
25°C 25°C
°C °C
Always estimate one digit beyond the last marking.

15. Now Let’s Practice Measuring and Converting
Units using the Factor-Label Method