What is the decimal representation of the fraction 1/5 (that is, one divided by five)?

Introduction:
This question asks you to convert a simple fraction, 1/5, into its decimal form. Such conversions are widely used in percentage problems, ratios, and everyday calculations where decimals are more convenient than fractions.

Given Data / Assumptions:

• Fraction: 1/5.
• We must express 1/5 as a decimal.
• We seek an exact, not approximate, decimal value.

Concept / Approach:
To convert a fraction a/b to a decimal, we perform the division a ÷ b. Because 5 is a factor of 10, 1/5 turns into a terminating decimal. Alternatively, we can use the known fact that 0.2 is equal to 1/5, but it is useful to see the division process clearly.

Step-by-Step Solution:
Step 1: Interpret the fraction as division: 1/5 = 1 ÷ 5.Step 2: Since 1 is smaller than 5, write it as 1.0 and then 1.00 as needed.Step 3: 5 goes into 10 exactly 2 times, because 2 * 5 = 10.Step 4: So 1.0 ÷ 5 = 0.2 exactly.Step 5: Writing this with three decimal places as in one of the options, 0.2 is the same as 0.200.Thus, the decimal representation is 0.200.

Verification / Alternative check:
Check by converting 0.2 back to a fraction: 0.2 = 2/10, and 2/10 simplifies to 1/5 when both numerator and denominator are divided by 2. This confirms that 0.2 (or 0.200) is exactly 1/5.

Why Other Options Are Wrong:
0.333 corresponds to approximately 1/3, not 1/5. 0.666 is about 2/3. 0.452 does not correspond to a simple fraction like 1/5. 0.500 is equal to 1/2, which is larger than 1/5. Only 0.200 matches the correct decimal for 1/5.

Common Pitfalls:
Some learners confuse 1/5 with 1/4 or 1/3 and may guess 0.25 or 0.333. Others may incorrectly think 1/5 equals 0.5 because of the number 5. Always remember that 1/5 means one part out of five equal parts, which is smaller than half, so its decimal must be less than 0.5.

Final Answer:
The fraction 1/5 expressed as a decimal is 0.200 (or simply 0.2).