Practice question · Sort into groups
Sort each number by whether it is rational or irrational.
Groups: Rational · Irrational
- the square root of 10
- 0.75
- the square root of 16
- 0.121212... repeating forever
- 0.1010010001... with an extra zero each time
- pi
- 22/7
Hints
- Simplify roots before judging, and check repeating decimals carefully.
- The last number never terminates AND never settles into a repeating block.
Show the answer
Rational: 0.75, the square root of 16, 0.121212... repeating forever, 22/7
Irrational: the square root of 10, pi, 0.1010010001... with an extra zero each time
Why
The square root of 16 is 4, and 22/7 is a ratio of integers even though it approximates pi, both rational. 0.121212... repeats, so it is rational too. The last decimal runs forever with an ever-growing gap between the 1s, so no block ever repeats: it is irrational. Endlessness alone never decides the question.
Practise Rational and Irrational Numbers
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