irrational

Everyday

1. Not based on clear thinking or good reasons (an irrational fear). tree →
2. (maths) An irrational number cannot be written as a fraction of two whole numbers, and its decimals go on forever without repeating, like pi or the square root of 2. tree →
3. Irrational can also describe a creature that cannot reason or think clearly. tree →

In the lessons

In everyday life: an irrational fear of spiders or of the dark, a choice made in anger. In maths (later school years): rational numbers are fractions; irrational numbers like pi and the square root of 2 are not. Phrases: irrational fear, irrational behaviour, irrational number.

Examples

• My fear of balloons popping is a bit irrational. tree →
• It is irrational to be angry at the rain. tree →
• Pi is an irrational number. tree →
• The square root of 2 is irrational: its decimals never end or repeat. tree →
• He made an irrational decision when he was tired. tree →
• Some fears are irrational, but they still feel real. tree →
• Jupiter, seeing that Mankind, the only rational creatures, were far outnumbered by the irrational beasts, bade him redress the balance by turning some of the latter into men. tree →

Note

Prefix ir- = not + rational. Double r. Opposite: rational. Math trap: 0.333... (repeating) is rational because it equals one third; only decimals that never end AND never repeat are irrational. 22/7 is close to pi but not equal to it.