Matter and Measurement: Units, Significant Figures, and Calculations

Chapter 2: Matter and Measurement

Units of Measurement

In chemistry, precise measurement is essential for describing matter and its changes. Scientists use standardized systems to ensure consistency and accuracy in measurements worldwide.

• Metric System: A decimal-based system of measurement used internationally.

• International System of Units (SI): The modern form of the metric system, adopted globally for scientific work.

• SI units are used for length, mass, volume, temperature, and time.

Table: Units of Measurement and Their Abbreviations

Measurement	Metric Unit	SI Unit
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)

Volume

Volume is the amount of space occupied by a substance. In chemistry, it is commonly measured in liters (L) and milliliters (mL).

• SI unit: cubic meter (m3), but liters and milliliters are more practical for laboratory use.

• 1 L = 1000 mL

• 1 L ≈ 1.06 qt

• 946 mL = 1 qt

Length

Length is measured in meters (m) in both the metric and SI systems. Chemists often use centimeters (cm) for convenience.

• 1 m = 100 cm

• 1 m ≈ 39.4 in.

• 1 m ≈ 1.09 yd

• 2.54 cm = 1 in.

Mass

Mass is a measure of the quantity of matter in an object. It is measured using a balance.

• SI unit: kilogram (kg)

• Chemists often use grams (g)

• 1 kg = 1000 g

• 1 kg ≈ 2.20 lb

• 454 g = 1 lb

Temperature

Temperature measures how hot or cold an object is. It is measured in degrees Celsius (°C) or kelvin (K).

• Water freezes at 0 °C (32 °F) and boils at 100 °C (212 °F).

• The Kelvin scale starts at absolute zero (0 K), the lowest possible temperature.

Measured Numbers vs. Exact Numbers

Numbers in chemistry can be classified as measured or exact:

• Measured numbers: Obtained using measuring tools; have a degree of uncertainty.

• Exact numbers: Obtained by counting or by definition; have no uncertainty and an infinite number of significant figures.

Table: Examples of Exact Numbers

Counted Numbers	Metric System	U.S. System
8 cookies	1 L = 1000 mL	1 ft = 12 in.
2 baseballs	1 kg = 1000 g	1 lb = 16 oz

Reporting Length and Measurement

When reporting the length of an object:

• Read the value at the end of the object using the marked lines (increments) on the measuring tool.

• Estimate the last digit by visually dividing the smallest marked interval into 10 equal parts.

• The reported measurement includes all certain digits plus one estimated digit.

Significant Figures (SFs)

Significant figures are all the digits in a measured number, including the estimated digit. They indicate the precision of a measurement.

• All nonzero digits are significant.

• Zeros may or may not be significant, depending on their position and the presence of a decimal point.

Table: Rules for Significant Figures

Rule	Example	Number of SFs
Nonzero digit	4.5	2
Zero between nonzero digits	205	3
Zero at the end of a decimal number	50.0	3
Zero at the beginning of a decimal number	0.002	1
Zero used as a placeholder in a large number without a decimal point	5000	1

Counting Significant Figures

To determine the number of significant figures in a measurement, apply the rules above. For example:

• 38.15 cm: 4 SFs

• 5.6 ft: 2 SFs

• 65.6 lb: 3 SFs

• 50.00 km: 4 SFs

• 8.0 × 103 g: 2 SFs

Significant Figures in Calculations

When performing calculations, the number of significant figures in the result depends on the operation:

• Multiplication/Division: The result has the same number of significant figures as the measurement with the fewest SFs.

• Addition/Subtraction: The result has the same number of decimal places as the measurement with the fewest decimal places.

Examples:

• $5.02 \times 89.665 \times 0.10 = 45.0118 \approx 45$ (2 SFs)

• $5.892 + 6.10 + 0.96590 = 12.9579 \approx 13.0$ (rounded to 1 decimal place)

Rules for 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.

Practice: Significant Figures

Apply the rules for significant figures and rounding to perform calculations:

• $1.10 \times 0.5120 \times 4.0015 \div 3.4555$

• $4.562 \times 3.99870 \div (452.6755 - 452.33)$

• Round each result to the correct number of significant figures.

Additional info: These foundational concepts are essential for all quantitative work in chemistry, ensuring that measurements and calculations are both accurate and precise.