Math CentralQuandaries & Queries


Question from owais, a teacher:

according to definition of irrational number "a number which cannot be
expressed in p/q form is called irrational number"
square root of 2 is a irrational number but if i round off the digit correct
to two decimal places so it becomes 1.41 and we can easily convert
into p/q form so it is a rational number ???
i have confusion plz help me


You are correct, 1.41 can easily be converted to a common fraction $\large \frac{p}{q}$ and hence it is a rational number. However 1.41 is not $\sqrt2,$ it is only an approximation of $\sqrt2.$ As you said it is only "correct to two decimal places".


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