SI Units & Metric Prefixes Cheat Sheet

Key Facts

• The SI base unit for length is the meter, written as $\text{m}$.
• The SI base unit for mass is the kilogram, written as $\text{kg}$, not the gram.
• The SI base unit for time is the second, written as $\text{s}$.
• Force is measured in newtons, and $1\ \text{N} = 1\ \text{kg}\cdot\text{m}/\text{s}^{2}$.
• Energy and work are measured in joules, and $1\ \text{J} = 1\ \text{N}\cdot\text{m} = 1\ \text{kg}\cdot\text{m}^{2}/\text{s}^{2}$.
• Power is measured in watts, and $1\ \text{W} = 1\ \text{J}/\text{s}$.
• Common metric prefixes include $\text{kilo} = 10^{3}$, $\text{centi} = 10^{-2}$, $\text{milli} = 10^{-3}$, $\text{micro} = 10^{-6}$, and $\text{mega} = 10^{6}$.
• To convert units, multiply by a fraction equal to $1$, such as $3.5\ \text{km}\times\frac{10^{3}\ \text{m}}{1\ \text{km}} = 3500\ \text{m}$.

Vocabulary

SI system

The international measurement system used in science, based on standard units such as $\text{m}$, $\text{kg}$, and $\text{s}$.

Base unit

A fundamental SI unit that is not made from other units, such as the meter $\text{m}$ or second $\text{s}$.

Derived unit

A unit made by combining base units, such as the newton $\text{N}$ or joule $\text{J}$.

Metric prefix

A symbol added before a unit to show a power of ten, such as $\text{k}$ for $10^{3}$ or $\text{m}$ for $10^{-3}$.

Conversion factor

A ratio equal to $1$ that changes a measurement from one unit to another without changing its value.

Dimensional analysis

A method for checking or converting units by tracking how units cancel in a calculation.