A fight to the death? A bit dramatic perhaps. š Engineering and scientific notation are both ways to simplify very large or small numbers so that they are easier to handle. In this article, we will explain and compare scientific vs engineering notation.
Scientific Notation
Putting annoyingly large or small numbers into scientific notation makes writing, calculating, and looking at numbers simpler. Scientific notation works by moving the decimal to get rid of excess zeros and then multiplying the number by 10 to the power of a non-zero number.
For example:
5,660,000 = 5.66×10^6
.00000566 = 5.66×10^-6
The exponent signifies how many places to move the decimal (negative to the left, positive to the right). There is also another format of scientific notation where the āx10ā is expressed by an āEā.
For example:
5,660,000 = 5.66E6
.00000566 = 5.66E-6
A number is only in correct scientific notation if there is only one digit to the left of the decimal. Scientific notation also helps with maintaining the correct number of significant figures. Significant figures are often used in science in order to keep numbers precise after numerous conversions and calculations.
Rules of significant figures:
- Any non-zero digit is significant
- Any zeros between significant figures are significant
- Trailing zeros are only significant to the right of the decimal point
So, the number 1,342,000 has four significant figures and would be converted to 1.342×10^6. The number 34,032 has five significant figures and would change to 3.4032×10^4.
Significant figures and scientific notation have played a huge role in my engineering classes, as they are often used in lab reports, homework, and research in order to maintain a more correct answer.
Engineering Notation
Engineering notation is very similar to scientific notation except for the fact that the exponent is always going to be a multiple of 3.
Example of engineering notation:
7,345,000 = 7.345×10^6
22,100,000,000 = 22.1×10^9
This is beneficial because it allows you to easily determine if a number is in the millions, billions, trillions, etc. If you saw the number 1.3×10^9 you could assume that the number is 1.3 trillion. If the exponent was a 6, you would know that it was 1.3 million.
Since the exponent is always a multiple of 3, engineering notation also helps when converting the number with a prefix when working with metric system units.
| Prefix | Symbol | Meaning | Engineering Notation |
| Giga | G | 1,000,000,000 | 10^9 |
| Mega | M | 1,000,000 | 10^6 |
| Kilo | k | 1,000 | 10^3 |
| Milli | m | .001 | 10^-3 |
| Micro | Ī¼ | .000001 | 10^-6 |
| Nano | n | .000000001 | 10^-9 |
So, if a number was 5.5×10^3 ( or 5,500 ) meters it could be converted to 5.5 kilometers. This can be very helpful when dealing with large or messy numbers during calculations and make it easier to produce a simplified answer.
Scientific vs. Engineering Notation
Determining whether to use engineering or scientific notation depends on how large/small your number is, what units you’re using, and what type of conversions you’re doing.
| Attribute | Scientific Notation | Engineering Notation |
| Industry | Most commonly used in science fields. Used in Chemistry because of the extremely small numbers. | Most often seen in the Electronic Industry because of the frequent use of SI units and prefixes. |
| Simplicity | Reduces number to only incorporate significant numbers | Easy to convert since the exponent is always a multiple of 3. |
| Popularity | Used in any profession where large or small numbers are used in mathematical calculations | Used by scientists, mathematicians, and engineers |
Generally speaking, scientific notation makes sense in a wider range of applications. Engineering notation best applies where orders of magnitude need to be conveyed to the reader swiftly.
