Is 0.2022022202222… rational or irrational, if the run of twos grows by one each time?
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
- Is rational or irrational, if the run of twos grows by one each time?
- What about , where the block repeats?
Need a reminder? The key ideaShow
An irrational number cannot be written as . Its decimal never ends and never repeats. is irrational when the whole number is not a perfect square. Rational and irrational numbers together make the real numbers.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Part (a). The runs of twos keep growing, so no fixed block repeats. The decimal never ends either. It is irrational.
Step 2. Part (b). The block repeats for ever, so it is rational. In fact it equals .
Answer: (a) irrational; (b) rational.
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