Mathematics — first biennium · Lesson
Irrational numbers are not 'impossible to calculate': they have a non-terminating non-repeating decimal expansion and can be approximated with controlled precision.
Prerequisites: Rational numbers and number line
Goal: Distinguish rational and irrational numbers and interpret approximation on the number line.
In this lesson: Distinguish rational and irrational numbers and interpret approximation on the number line.
New concept: An irrational number cannot be written as a ratio of two integers. When we represent it with a finite decimal, we are using an approximation, not its exact value.
How to proceed: First find two consecutive perfect squares bracketing the radicand; the approximation must stay between those two integers.
You can already assume: Rational numbers and number line.
Completed exercises: 0/5 · Correct on first attempt: 0
First find two consecutive perfect squares bracketing the radicand; the approximation must stay between those two integers.
Data / situation: Consider √5.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.