Chapter E Units, Measurement, and Problem Solving

Units & Measurements

SI unit for length → meter (m)

SI unit for mass → kilogram (kg)

SI unit for time → second (s)

SI unit for temperature → kelvin (K)

Mass → Amount of matter.

Weight → Force of gravity on matter.

Derived unit → Combination of base units.

Metric Conversions

kilo (k) → 10³

centi (c) → 10⁻²

milli (m) → 10⁻³

micro (μ) → 10⁻⁶

nano (n) → 10⁻⁹

pico (p) → 10⁻¹²

1 L → 1 dm³

1 mL → 1 cm³

Density

Density formula → d = m/V

Mass formula → m = dV

Volume formula → V = m/d

Common density units → g/mL or g/cm³

Measurement & Uncertainty

Exact number → Known exactly; no uncertainty.

Inexact number → Measured; has uncertainty.

Accuracy → Close to the true value.

Precision → Measurements close to each other.

Measured value rule → Last reported digit is uncertain/estimated.

Significant Figures ⭐

Nonzero digits → Always significant.

Zeros between nonzero digits → Significant.

Leading zeros → NOT significant.

Trailing zeros after a decimal → Significant.

Addition/Subtraction rule → Least decimal places.

Multiplication/Division rule → Fewest sig figs.

When to round? → At the end of the calculation.

Temperature Formulas

Celsius → Kelvin → K = °C + 273.15

Celsius → Fahrenheit → °F = (9/5)(°C) + 32

Fahrenheit → Celsius → °C = (5/9)(°F − 32)

Energy

Energy → Capacity to do work.

Kinetic energy → Energy of motion.

Potential energy → Stored energy.

SI energy unit → joule (J)

1 cal → 4.184 J

Conservation of energy → Energy cannot be created or destroyed.

Exothermic → Energy leaves the system.

Endothermic → Energy enters the system.

Memory: EXO = EXits. ENDO = ENters.

Dimensional Analysis ⭐

Dimensional analysis → Using conversion factors to change units.

Conversion factor → Ratio of two equivalent quantities.

Main rule → Set up conversion factors so unwanted units cancel.

Problem-solving method → What do I have? → What do I want? → What conversion do I need?

Squared/cubed unit conversion → Raise the number AND unit to the power.

🔥 Highest Priority to Know

If you're short on study time, focus hardest on:

d = m/V
Metric prefixes
Accuracy vs. precision
Exact vs. inexact numbers
Sig-fig rules
+ / − → decimal places
× / ÷ → sig figs
Temperature conversion formulas
Exothermic vs. endothermic
Dimensional analysis/unit cancellation