Chemistry and Measurements: Units, Significant Figures, and Conversion Factors

Chemistry and Measurements

Introduction

This chapter introduces the foundational concepts of measurement in chemistry, including the use of metric and SI units, significant figures, and the application of conversion factors. Mastery of these topics is essential for accurate scientific calculations and laboratory work in General, Organic, and Biological (GOB) Chemistry.

Units of Measurement

Metric and SI Units

Chemists use standardized units to ensure consistency in measurements. The metric system and the International System of Units (SI) are the most widely used systems.

• Volume: liter (L) [metric], cubic meter (m3) [SI]

• Length: meter (m) [both systems]

• Mass: gram (g) [metric], kilogram (kg) [SI]

• Temperature: degree Celsius (°C) [metric], kelvin (K) [SI]

• Time: second (s) [both systems]

Measurement	Metric	SI
Volume	liter (L)	cubic meter (m3)
Length	meter (m)	meter (m)
Mass	gram (g)	kilogram (kg)
Temperature	degree Celsius (°C)	kelvin (K)
Time	second (s)	second (s)

Measured Numbers and Significant Figures

Measured Numbers

Measured numbers are obtained using measuring tools and always contain some degree of uncertainty. The last digit in a measured value is estimated.

• Example: Measuring a length as 4.55 cm means the last digit (5) is estimated.

Significant Figures (Sig Figs)

Significant figures include all known digits plus one estimated digit in a measured number.

• Rules for Significant Figures:

  1. All nonzero digits are significant.

  2. Interior zeros (between nonzero digits) are significant.

  3. Trailing zeros after a decimal point are significant.

  4. Trailing zeros before an implied decimal point are ambiguous (usually not significant).

  5. Leading zeros (before the first nonzero digit) are not significant.

Measurement	Number of Significant Figures
38.15 cm	4
0.440 km	3
50.08 km	4
44,000 km	2 (ambiguous)

Scientific Notation and Significant Figures

When writing numbers in scientific notation, only significant digits are included in the coefficient.

• Example: 0.002650 m = $2.650 \times 10^{-3}$ m (four significant figures)

Exact Numbers

Exact numbers are obtained by counting or by definition (e.g., 1 dozen = 12 items). They have an unlimited number of significant figures and do not affect calculations involving significant figures.

Items	Metric System	U.S. System
8 doughnuts	1 L = 1000 mL	1 ft = 12 in.
5 capsules	1 kg = 1000 g	1 lb = 16 oz

Significant Figures in Calculations

Multiplication and Division

The result should have the same number of significant figures as the measurement with the fewest significant figures.

• Example: $5.00 \times 3.408 \div 2.0 = 8.5$ (2 significant figures)

Addition and Subtraction

The result should have the same number of decimal places as the measurement with the fewest decimal places.

• Example: $82.409 + 22.0 = 104.4$ (rounded to the tenths place)

Rounding Off

• If the first digit to be dropped is 4 or less, drop it and all following digits.

• If the first digit to be dropped is 5 or greater, increase the last retained digit by 1.

Prefixes and Equalities

Metric and SI Prefixes

Prefixes are used to indicate multiples or fractions of units in the metric and SI systems.

Prefix	Symbol	Value	Scientific Notation	Equality
kilo	k	1,000	$10^3$	1 km = $1 \times 10^3$ m
centi	c	0.01	$10^{-2}$	1 cm = $1 \times 10^{-2}$ m
milli	m	0.001	$10^{-3}$	1 mm = $1 \times 10^{-3}$ m
micro	μ	0.000001	$10^{-6}$	1 μg = $1 \times 10^{-6}$ g
nano	n	0.000000001	$10^{-9}$	1 nm = $1 \times 10^{-9}$ m

Equalities

Equalities show the relationship between two units that measure the same quantity. They can be within the metric system, U.S. system, or between the two.

• Examples:

  • 1 m = 100 cm = $1 \times 10^2$ cm

  • 1 L = 1000 mL = $1 \times 10^3$ mL

  • 1 kg = 2.20 lb

  • 1 in. = 2.54 cm (exact)

Writing and Using Conversion Factors

Conversion Factors

Any equality can be written as two conversion factors (fractions) that relate the two units.

• Example: 1 h = 60 min can be written as $\frac{60\,\text{min}}{1\,\text{h}}$ or $\frac{1\,\text{h}}{60\,\text{min}}$

Common Equalities Table

Quantity	Metric (SI)	U.S.	Metric-U.S.
Length	1 km = 1000 m	1 ft = 12 in.	2.54 cm = 1 in. (exact)
Volume	1 L = 1000 mL	1 qt = 4 cups	1 L = 1.06 qt
Mass	1 kg = 1000 g	1 lb = 16 oz	1 kg = 2.20 lb
Time	1 min = 60 s	1 h = 60 min

Conversion Factors in Practice

• Conversion factors are used to convert between units in calculations.

• In multi-step problems, two or more conversion factors may be needed.

• Example: To convert 2.44 m to cm: $2.44 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 244 \text{ cm}$

Density and Specific Gravity

Density

Density is the ratio of the mass of a substance to its volume. It is a physical property used to identify substances and solve problems involving mass and volume.

• Formula: $\text{Density} = \frac{\text{mass}}{\text{volume}}$

• Units: g/cm3 (solids), g/mL (liquids), g/L (gases)

• Example: A 48.0-g sample increases water volume from 25.0 mL to 33.0 mL. Density = $\frac{48.0\,\text{g}}{8.0\,\text{mL}} = 6.0\,\text{g/mL}$

Specific Gravity

Specific gravity is the ratio of the density of a substance to the density of water (1.00 g/mL at 4°C). It is a unitless quantity often used in clinical settings.

• Formula: $\text{Specific Gravity} = \frac{\text{density of sample}}{\text{density of water}}$

• Application: Used to assess urine concentration in medical diagnostics.

Summary Table: Key Concepts

Concept	Definition/Rule	Example
Significant Figures	All known digits plus one estimated digit	4.55 cm (3 sig figs)
Density	Mass per unit volume	$\frac{48.0\,\text{g}}{8.0\,\text{mL}} = 6.0\,\text{g/mL}$
Conversion Factor	Fraction relating two units	$\frac{100\,\text{cm}}{1\,\text{m}}$
Specific Gravity	Density of sample / Density of water	$\frac{1.32\,\text{g/mL}}{1.00\,\text{g/mL}} = 1.32$

Additional info:

• Practice problems and learning checks are included throughout the chapter to reinforce understanding of significant figures, unit conversions, and density calculations.

• Clinical applications, such as bone density and urine specific gravity, highlight the relevance of these concepts in health sciences.