recall and use the following prefixes and their symbols to indicate decimal submultiples or multiples of both base and derived units: pico (p), nano (n), micro ( μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)

SI Units – Decimal Prefixes

In the International System of Units (SI) prefixes are used to express very large or very small quantities in a compact form. Each prefix represents a power of ten and has a standard symbol that is placed directly before the unit symbol.

List of Common Prefixes

• pico – symbol p – \$10^{-12}\$
• nano – symbol n – \$10^{-9}\$
• micro – symbol μ – \$10^{-6}\$
• milli – symbol m – \$10^{-3}\$
• centi – symbol c – \$10^{-2}\$
• deci – symbol d – \$10^{-1}\$
• kilo – symbol k – \$10^{3}\$
• mega – symbol M – \$10^{6}\$
• giga – symbol G – \$10^{9}\$
• tera – symbol T – \$10^{12}\$

Reference Table

Using Prefixes with Base Units

Base units are the fundamental SI units such as metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol) and candela (cd). To apply a prefix, simply place the prefix symbol directly before the unit symbol.

1. Identify the quantity you need to express.
2. Choose a prefix that brings the numeric value into a convenient range (typically 0.1 to 1000).
3. Multiply or divide by the appropriate power of ten.
4. Write the result using the prefix symbol.

Examples

Example 1 – Length

Convert \$0.00045\ \text{m}\$ to an appropriate SI prefix.

Solution:

1. Recognise that \$0.00045\ \text{m}=4.5\times10^{-4}\ \text{m}\$.
2. The nearest power of ten that matches a prefix is \$10^{-3}\$ (milli).
3. Divide by \$10^{-3}\$: \$\displaystyle \frac{4.5\times10^{-4}\ \text{m}}{10^{-3}} = 0.45\ \text{mm}\$.
4. Result: \$0.45\ \text{mm}\$.

Example 2 – Energy

Express \$3.2\times10^{6}\ \text{J}\$ using a suitable prefix.

Solution:

1. The factor \$10^{6}\$ corresponds to the prefix mega (M).
2. Divide by \$10^{6}\$: \$\displaystyle \frac{3.2\times10^{6}\ \text{J}}{10^{6}} = 3.2\ \text{MJ}\$.
3. Result: \$3.2\ \text{MJ}\$.

Example 3 – Derived Unit (Power)

Convert \$0.025\ \text{W}\$ to a more convenient form.

Solution:

1. \$0.025\ \text{W}=2.5\times10^{-2}\ \text{W}\$.
2. The prefix deci (d) corresponds to \$10^{-1}\$, but the value is still small.
3. Using milli (m) which is \$10^{-3}\$: \$\displaystyle \frac{2.5\times10^{-2}\ \text{W}}{10^{-3}} = 25\ \text{mW}\$.
4. Result: \$25\ \text{mW}\$.

Applying Prefixes to Derived Units

Derived units are formed from base units (e.g., newton N = kg·m·s⁻², joule J = N·m). Prefixes are applied in the same way as for base units.

Practice Questions

1. Write \$7.8\times10^{-9}\ \text{F}\$ using an appropriate SI prefix.
2. Convert \$5\ \text{km}\$ to metres and then express the result using the most suitable prefix.
3. A power rating is \$2.5\times10^{3}\ \text{W}\$. Express this in kilowatts.
4. Express \$0.00012\ \text{g}\$ in micrograms.