Question 40 of 58intermediate💡 UnderstandShort Answer6 marks

Classify the following numbers as rational or irrational. Find the explicit fractions in case they are rational.

(i)

81\sqrt{81}

Answer

Rational; Explicit fraction: 9/1

(ii)

12\sqrt{12}

Answer

Irrational

(iii)

0.33333…0.33333 \ldots

Answer

Rational; Explicit fraction: 1/3

(iv)

0.123451234512345…0.123451234512345 \ldots

Answer

Rational; Explicit fraction: 12345/99999

(v)

1.01001000100001…1.01001000100001 \ldots (Notice the pattern: Is it repeating a single block?)

Answer

Irrational

(vi)

23.56018561223987479012023.560185612239874790120

Answer

Rational; Explicit fraction: 23560185612239874790120/1000000000000000000000

Explanation

A rational number is defined as any number that can be expressed in the form p/q, where p and q are integers and q ≠\neq 0. Rational numbers have decimal expansions that are either terminating or non-terminating and repeating. Irrational numbers have non-terminating, non-repeating decimal expansions. We evaluate each number based on these properties to classify them and find their explicit fractions if applicable.

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