Which of the following is a rational number?

Introduction / Context:
This question tests understanding of rational numbers and how they relate to decimal representations. A rational number is any number that can be expressed as a fraction p/q where p and q are integers and q is not zero. In decimal form, rational numbers either terminate after a finite number of digits or repeat a block of digits indefinitely. We must decide which of the given decimal and integer options are rational.

Given Data / Assumptions:

• Option 0.241 is a terminating decimal.
• Option 1.732 is given as a decimal with three places.
• Option 4 is an integer.
• We assume the decimals are exact as written (not approximate symbols like square roots), unless explicitly stated otherwise.
• We must identify which options represent rational numbers.

Concept / Approach:
By definition, a terminating decimal can always be written as a fraction with denominator a power of 10, which makes it rational. Any integer n can be written as n/1, so integers are also rational. Thus, if 0.241 and 1.732 are taken as exact decimals, both are rational. The question is testing whether we recognise that decimal notation without a bar still represents rational numbers when they terminate at a finite place, and that integers are rational by default.

Step-by-Step Solution:
Step 1: Consider 0.241. This is a terminating decimal with three digits after the decimal point.Step 2: We can write 0.241 as 241/1000, since moving the decimal three places to the right gives 241, and the denominator becomes 10^3 = 1000.Step 3: Because 241 and 1000 are integers and the denominator is nonzero, 0.241 is a rational number.Step 4: Consider 1.732. As written, it is a terminating decimal with three digits after the decimal point.Step 5: We can express 1.732 as 1732/1000 by similar reasoning, or further simplify the fraction if desired. In any case, it can be written as p/q with integers p and q, so 1.732 is rational.Step 6: Consider 4. This is an integer and can be written as 4/1, which matches the definition of a rational number.Step 7: Since all three listed numbers are rational, the correct choice is "All of the above".

Verification / Alternative check:
To reinforce the idea, recall that irrational numbers are those that cannot be expressed as a fraction of integers, and their decimal expansions neither terminate nor repeat (for example, the exact values of √2 or π). In contrast, a decimal like 1.732, written with a fixed number of decimal places, is always equal to some fraction with denominator 10^3. Thus it is rational. Only if the question explicitly indicated that 1.732 represents an irrational expression like the square root of 3 would we consider it irrational. As stated, it is just a finite decimal.

Why Other Options Are Wrong:
Option 0.241 only: Choosing this alone ignores the fact that 1.732 and 4 are also rational.Option 1.732 only: This also undercounts; integers and other terminating decimals remain rational.Option 4 only: While 4 is rational, so are the other two numbers.Option None of these: This would imply none of the numbers is rational, which contradicts all the reasoning above.

Common Pitfalls:
Students sometimes associate 1.732 with an approximation to √3 and mistakenly classify it as irrational, forgetting that the decimal 1.732 exactly as written is a terminating decimal and therefore rational. Others forget that every integer is automatically a rational number. Always remember: any terminating decimal or repeating decimal can be written as a fraction of integers and is rational, and every whole number is rational as well.

Final Answer:
The rational number(s) among the options are All of the above.