# Is -5 a rational or irrational?

Asked on by tealseal

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

A rational number is a real number that can be expressed in the form of fraction p/q, where both p and q are any integers. These integers can be either positive or negative. However, q cannot be equal to zero.

Since -5 can be expressed as the fraction  -5/1, it is a rational number.

Opposite of rational number is irrational number that cannot be expressed in the form p/q. This means that irrational numbers can not be represented with absolute accuracy as decimal numbers with limited digits. Some example of irrational numbers are Pi, square root of 2, cube root of 3, and cube root of 11. Please note that irrational numbers cannot be expressed correctly as a fraction

william1941 | College Teacher | (Level 3) Valedictorian

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A rational number is one that can be expressed in the form p/q where p and q are two integers. Now integers can be positive as well as negative.

An irrational number is one which cannot be written in the form p/q where p and q are integers. These include numbers like sqrt 5 among many others. It is not possible to find any set of p and q such that 5= p^2/ q^2. So sqrt 5 is an irrational number.

We can write -5 as -5/1 or in many other ways using only integers. Therefore -5 is a rational number.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

-5 is a rational number.

A  number is rational if it can be written as p/q , where p and q are integers, positive or negative.

- 5 = -5/1 or -10/2. etc where numerator and denominators are both integers.

2^(1/2) or sqrt5,  3^(2/3) etc are not integers as they cannot be completely (not approximately) expressed in the form of a fraction like p/q, where both p and q are integers.

sqrt9 or 9^(1/3) = 3 = 3/1 is in p/q form . So 9^(1/3)  is rational.

sqrt(25/9) = (25/9)^(1/2) = 5/3 is in p/q form. So sqrt(25/9) is rational.

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