Expression 0.612 in the form $\frac{x}{y}$, where x and y are integers and y $\neq$ 0

Analyze the question: We need to write the decimal 0.612 as a fraction in the form x/y.

Concept: A terminating decimal with 3 decimal places can be written over 1000, then simplified. (If the decimal were recurring, such as 0.612612..., we would use a different method. The question as written shows a plain 0.612, so it is terminating.)

Solution:

0.612 = 612/1000

Find the HCF of 612 and 1000. Both are divisible by 4:

• 612 ÷ 4 = 153
• 1000 ÷ 4 = 250

So 0.612 = 153/250.

Check whether it simplifies further: 153 = 9 × 17 = 3² × 17, and 250 = 2 × 5³. They share no common factor, so 153/250 is in its simplest form.

Check the other options:

• B. 68/111 = 0.612612... (a recurring decimal, 0.6̇1̇2̇), not 0.612 exactly.
• C. 61/100 = 0.61, which is wrong.
• D. 21/33 = 7/11 = 0.636..., which is wrong.

Note that option B equals 0.612 only if the decimal is recurring. The question as given has no recurring dots, so the correct answer is A. (If the original paper had dots over the digits, B would be the answer.)

Tip: For a terminating decimal, write it over 10, 100, 1000 and so on, depending on the number of decimal places, and then divide top and bottom by their HCF. For recurring decimals, multiply by 10, 100 or 1000 and subtract.