Which of the following is the fraction equivalent to 2.04?

2023

Which of the following is the fraction equivalent to 2.04?

  1. A.

    1/25

  2. B.

    51/25

  3. C.

    12/5

  4. D.

    51/250

Attempted by 3 students.

Show answer & explanation

Correct answer: B

Concept: To convert a decimal into a fraction, write it as (digits)/(power of 10 matching the number of decimal places), then simplify by dividing both terms by their HCF.

Application:

  1. 2.04 has 2 digits after the decimal point, so the denominator will be 100.

  2. Write 2.04 as 204/100 (multiply by 100 to clear the decimal point, keeping the denominator as 100).

  3. Find the HCF of 204 and 100: HCF(204, 100) = 4.

  4. Divide both numerator and denominator by 4: 204 ÷ 4 = 51, 100 ÷ 4 = 25.

  5. Result: 51/25, already in lowest terms since HCF(51, 25) = 1.

Cross-check: 51 ÷ 25 = 2.04, confirming the conversion. Also, 25 = 5² and 51 = 3 × 17 share no common factor, so the fraction is fully reduced.

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