M4.1.6 For the adult
Rational and irrational numbers
Is a decimal that never ends, such as 0.272727..., really a fraction?
What this chapter teaches
A rational number is a fraction of two whole numbers, and every decimal that stops or repeats is one. To turn a repeating decimal into a fraction, multiply by a power of ten that matches the length of the repeat, then subtract. An irrational number such as √2 or π cannot be written that way. This has nothing to do with how long the decimal is.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why do we multiply 0.2727... by 100 and not by 10?
- Is 1/7 rational or irrational, even though its decimal is long?
- What does it mean to say that √2 is irrational?
After the chapter, the learner can
- Change a repeating decimal like 0.272727... into a fraction
- Tell rational numbers from irrational ones like √2 and π
What they copy into their notebook
Rational: a fraction of whole numbers. Repeating decimals are rational: multiply by 10 to the repeat length, subtract x. Irrational: no such fraction, like √2 and π.