BeginnerTopic 4 of 104Engineering Mathematics
Scientific notation
Writing numbers as a x 10^n makes very large or small quantities compact and easy to compare.
In depth
Scientific notation writes a number as m×10ⁿ with 1≤m<10. Engineering notation restricts the exponent to multiples of three so it maps to SI prefixes such as kilo, mega and milli. It makes comparison of magnitudes and multiplication of very large or small numbers simple.
Key points
- Add exponents when multiplying
- Subtract exponents when dividing
- Prefixes: k=10³, M=10⁶, µ=10⁻⁶, n=10⁻⁹
Example4.7 kΩ = 4.7×10³ Ω and 22 nF = 2.2×10⁻⁸ F.
What is Scientific notation?
Writing numbers as a x 10^n makes very large or small quantities compact and easy to compare.
Why is it important to understand scientific notation?
Engineering quantities range from nanometres to light-years, and scientific notation keeps those numbers readable and prevents typing errors.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then renormalise so the coefficient lies between 1 and 10.
Is 0.00045 better written as 4.5 × 10⁻⁴?
Yes. It shows the magnitude at a glance and makes the number of significant figures clear.
How is Scientific notation used in practice?
Typical applications include entering a capacitance of 4.7×10⁻⁶ F in a simulator, comparing the stiffness of steel and rubber on one chart and expressing a large data-centre energy total in kWh.
What should I learn before Scientific notation?
Study "Units and dimensional analysis" first (topic 3 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
What are the key points of Scientific notation?
Add exponents when multiplying. Subtract exponents when dividing. Prefixes: k=10³, M=10⁶, µ=10⁻⁶, n=10⁻⁹.
Can you give an example of Scientific notation?
4.7 kΩ = 4.7×10³ Ω and 22 nF = 2.2×10⁻⁸ F.
What comes after Scientific notation?
The next topic is "Ratios, proportions and percentages", which builds directly on this one.
How difficult is Scientific notation?
It is classed as Beginner in Engineering Mathematics (topic 4 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.