Chemistry and Measurements: Units, Significant Figures, and Calculations

Chemistry and Measurements

Introduction

Chemistry relies on precise measurements to describe matter and its changes. Understanding units, significant figures, and the rules for calculations is essential for accurate scientific communication and problem-solving in General, Organic, and Biological (GOB) Chemistry.

Units of Measurement

Metric and SI Units

• Metric System: A decimal-based system used globally for scientific measurements.

• International System of Units (SI): The official system of measurement for length, volume, mass, temperature, and time.

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)

Examples and Applications

• Graduated cylinders measure volume in mL and L.

• Rulers measure length in cm and m.

• Balances measure mass in g and kg.

• Thermometers measure temperature in °C and K.

• Stopwatches measure time in s, min, and h.

Measured Numbers and Significant Figures

Measured Numbers

• Obtained by measuring a quantity (e.g., height, weight, temperature).

• Include all certain digits plus one estimated digit.

Significant Figures (SFs)

• All nonzero digits are significant.

• Zeros between nonzero digits are significant.

• Zeros at the end of a decimal number are significant.

• Zeros used as placeholders (before digits or at the end of large numbers without a decimal) are not significant.

Rule	Measured Number	Number of SFs
Not a zero	4.5 g	2
Zero between nonzero digits	205 °C	3
Zero at the end of a decimal	16.00 mL	4
Zero at the beginning of a decimal	0.0004 s	1
Zero as placeholder in large number	850 000 m	2

Scientific Notation

• Used to clearly indicate significant zeros in large or small numbers.

• Example: 0.002 650 m = $2.650 imes 10^{-3}$ m (4 SFs)

Exact Numbers

• Obtained by counting or defined relationships (e.g., 1 kg = 1000 g).

• Have an unlimited number of significant figures.

Significant Figures in Calculations

Rounding Off

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

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

Multiplication and Division

• The answer has the same number of SFs as the measurement with the fewest SFs.

• Example: $24.66 imes 0.35 = 8.6$ (2 SFs)

Addition and Subtraction

• The answer has the same number of decimal places as the measurement with the fewest decimal places.

• Example: $66.102 + 0.30 = 66.1$ (rounded to tenths place)

Appendix: Example Measurements

• Temperature: 22°C (72°F)

• Backpack mass: 12 kg (26 lb)

• Body mass: 58.0 kg (128 lb)

• Height: 1.7 m (65 in.)

• Distance: 2.1 km (1.3 mi)

Summary Table: SI Units for Common Quantities

Quantity	SI Unit
Volume	cubic meter (m3)
Mass	kilogram (kg)
Length	meter (m)
Temperature	kelvin (K)

Key Takeaways

• Always use the correct units and significant figures in measurements and calculations.

• Understand the difference between measured and exact numbers.

• Apply the rules for significant figures to ensure accuracy in scientific work.