Chapter 2: Standards for Measurement

Overview

• Focus on careful, accurate measurements in both cooking and chemistry labs.

Chapter Outline

1. Scientific Notation
2. Measurement and Uncertainty
3. Significant Figures
   • Rounding off numbers
4. Significant Figures in Calculations
   • Addition, Subtraction, Multiplication, Division
5. The Metric System
   • Length, Mass, Volume
6. Dimensional Analysis
7. Percent Calculations
8. Measurement of Temperature
9. Density

2.1 Scientific Notation

• Uses powers of 10 for large/small numbers.
• Steps:
  1. Move decimal after first nonzero digit.
  2. Multiply by 10^positions moved.
  3. Positive/negative exponent shows direction moved.

2.2 Measurement and Uncertainty

• Measurements include numerical value and unit.
• Uncertainty exists in estimated last digit.
• Significant Figures: Certain digits + 1 estimated digit.

2.3 Significant Figures

• Rules:
  1. All nonzero digits significant.
  2. Exact numbers (e.g., 12 inches) have infinite sig figs, no uncertainty.
  3. Zeroes significant when:
     • Between nonzero digits (e.g., 75.04)
     • After decimal point (e.g., 32.410)
  4. Zeroes not significant when:
     • Before first nonzero digit (e.g., 0.00321)
     • End of number without decimal point
• Use scientific notation for clarity.

Rounding Off Numbers

• Calculator results may exceed proper sig figs.
• Rules:
  • First digit <5: do not change last retained digit.
  • First digit ≥5: increase last retained digit by one.

2.4 Significant Figures in Calculations

• Precision limited by least precise measurement.
• Multiplication/Division: Answer based on least sig figs.
• Addition/Subtraction: Answer based on least precision.

2.5 The Metric System

• SI Units:
  • Length: meter (m)
  • Mass: kilogram (kg)
  • Volume: cubic meter (m³), liter (L)
  • Temperature: Kelvin (K)
• Prefixes: Giga (G), Mega (M), Kilo (k), Milli (m), Micro (µ), etc.

2.6 Dimensional Analysis

• Converts units using conversion factors.
• Example: Convert km to m using factor 1000 m/1 km.

2.7 Percent

• Formula: (parts/total parts) x 100%
• Used in mixture compositions, mass percent calculations.

2.8 Measurement of Temperature

• Scales: Celsius, Fahrenheit, Kelvin.
• Conversions:
  • K = °C + 273.15
  • °F = (9/5)°C + 32

2.9 Density

• Formula: Density = mass/volume
• Units: g/mL (liquids/solids), g/L (gases)
• Density changes with temperature.

Learning Objectives

• Use scientific notation and understand measurement uncertainty.
• Apply rules for significant figures.
• Convert units in the metric system and solve problems using dimensional analysis.
• Work with percent, temperature scales, and density.