BeginnerTopic 1 of 104Engineering Mathematics
Number systems
Engineers use natural, integer, rational, real and complex numbers; each extends the previous to solve equations the smaller set cannot.
In depth
Naturals count, integers add negatives, rationals are ratios of integers, reals fill the number line including irrational numbers like √2 and π, and complex numbers add the imaginary unit i. Engineers pick the smallest set that can represent the quantity at hand.
Key points
- Every set contains the previous one
- Computers store reals approximately as floating point
- Complex numbers are needed for AC and vibrations
ExampleThe equation x²+1=0 has no real solution but has the complex solutions ±i.
Every measurement, model and computer number lives in one of these sets, so knowing which one you are in tells you which operations are safe.
What is Number systems?
Engineers use natural, integer, rational, real and complex numbers; each extends the previous to solve equations the smaller set cannot.
Why is it important to understand number systems?
Every measurement, model and computer number lives in one of these sets, so knowing which one you are in tells you which operations are safe.
Why do engineers need complex numbers if no physical quantity is imaginary?
Complex numbers are a bookkeeping tool. They store amplitude and phase together, which makes AC circuits and waves far easier to calculate.
What is the difference between rational and irrational numbers in practice?
Rational numbers can be written exactly as fractions, while irrational numbers such as π or √2 need rounding in any digital calculation.
How is Number systems used in practice?
Typical applications include choosing a data type for an embedded sensor reading, recognising that a square root of a negative number needs complex numbers in AC analysis and reading the precision limits of a microcontroller integer.
What should I learn before Number systems?
It is the first topic in Engineering Mathematics, so no earlier topic in this course is required.
What are the key points of Number systems?
Every set contains the previous one. Computers store reals approximately as floating point. Complex numbers are needed for AC and vibrations.
Can you give an example of Number systems?
The equation x²+1=0 has no real solution but has the complex solutions ±i.
What comes after Number systems?
The next topic is "Significant figures", which builds directly on this one.
How difficult is Number systems?
It is classed as Beginner in Engineering Mathematics (topic 1 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.