Proper engineering notation is a specialized form of scientific notation where the exponent of the base ten is always a multiple of three. This convention greatly simplifies the representation and understanding of very large or very small numbers, particularly in technical fields like electronics, physics, and engineering.
Understanding the Core Concept
The fundamental difference between engineering notation and standard scientific notation lies solely in the exponent. While scientific notation allows any integer exponent for the power of ten (e.g., 4.5 x 10^10), engineering notation insists that this exponent must be a multiple of three (..., -9, -6, -3, 0, 3, 6, 9, ...).
For example:
- 45E9 (which represents 45 x 10^9) is considered proper engineering notation because 9 is a multiple of three.
- 4.5E10 (4.5 x 10^10), while mathematically equivalent to 45E9, is not proper engineering notation because 10 is not a multiple of three.
Key Characteristics and Benefits
Engineering notation is designed for practical application, making values easy to read and relate to standard SI prefixes.
- Exponent Rule: The exponent of 10 must be a multiple of three (e.g., 10^3, 10^6, 10^-3, 10^-9).
- Mantissa (Coefficient) Range: To adhere to the exponent rule, the mantissa (the number multiplied by the power of ten) will typically fall within the range of 1 to 999 (inclusive). For instance, instead of 1.2 x 10^4 (scientific), it would be 12 x 10^3 (engineering).
- Direct Relation to SI Prefixes: This is the most significant advantage. Each multiple of three exponent directly corresponds to a common SI prefix, such as kilo (10^3), mega (10^6), giga (10^9), milli (10^-3), micro (10^-6), and nano (10^-9). This makes unit conversions and quantity comparisons much more intuitive.
Practical Examples
Let's illustrate how numbers are expressed in engineering notation:
- Large Number: To express 123,450,000,000 Hertz (Hz):
- In scientific notation: 1.2345 x 10^11 Hz
- In engineering notation: 123.45 x 10^9 Hz (or 123.45 GHz)
- Small Number: To express 0.0000000047 Farads (F):
- In scientific notation: 4.7 x 10^-9 F
- In engineering notation: 4.7 x 10^-9 F (or 4.7 nF) – In this case, both are the same as -9 is already a multiple of three.
- Medium Number: To express 45,670 Ohms (Ω):
- In scientific notation: 4.567 x 10^4 Ω
- In engineering notation: 45.67 x 10^3 Ω (or 45.67 kΩ)
Calculator Representation
On most scientific calculators, the "E" that represents "times ten to the power of" is commonly denoted by either an "EE" or "EXP" button. When entering a number like 45E9, you would typically press 45, then the EE or EXP button, and finally 9.
Common SI Prefixes and Engineering Notation
The close relationship between engineering notation and SI prefixes is vital for clear communication in technical fields.
| Exponent (Power of 10) | SI Prefix | Symbol | Example (Engineering Notation) |
|---|---|---|---|
| 10^12 | Tera | T | 5 TΩ (5 x 10^12 Ohms) |
| 10^9 | Giga | G | 1.5 GHz (1.5 x 10^9 Hertz) |
| 10^6 | Mega | M | 22 MΩ (22 x 10^6 Ohms) |
| 10^3 | Kilo | k | 47 kΩ (47 x 10^3 Ohms) |
| 10^0 | (none) | 123 Ohms (123 x 10^0 Ohms) | |
| 10^-3 | Milli | m | 3.3 mA (3.3 x 10^-3 Amperes) |
| 10^-6 | Micro | μ | 10 μF (10 x 10^-6 Farads) |
| 10^-9 | Nano | n | 220 nF (220 x 10^-9 Farads) |
| 10^-12 | Pico | p | 12 pF (12 x 10^-12 Farads) |
By adhering to the rule of using exponents that are multiples of three, engineering notation provides a consistent and highly readable way to express numerical values across a vast range of magnitudes, making calculations and understanding much more straightforward for professionals.
