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Q.

Which of the following is irrational?

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a

\frac{1}{3}

b

\frac{48}{5}

c

0.7777 \dots

d

1.73202002 \dots

answer is D.

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Detailed Solution

Given numbers are,

\frac{1}{3}

,

\frac{48}{5}

,

0.7777 \dots

and

1.73202002 \dots

Rational numbers are numbers that are expressed as fractions. They can be positive, negative or zero. Rational numbers are of the form

\frac{p}{q}

, where q≠0. Rational numbers can be non-terminating and repeating.
Irrational numbers are numbers that cannot be expressed as fractions. Irrational numbers are non-terminating and non-repeating decimal numbers.
Thus, 0.7777….. is a rational number, only

1.73202002 \dots

is an irrational number as it is non-terminating and non repeating.
Therefore, option (4) is correct.

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