What is the decimal representation of the fraction 1/8, written as an exact terminating decimal value?

Introduction / Context:
Fractions and decimals are two different notations for the same rational numbers. This question checks whether you can convert a simple fraction with denominator eight into its exact decimal form, which is a common skill in aptitude tests, banking, and everyday calculations.

Given Data / Assumptions:

• Given fraction: 1/8.
• We need to write 1/8 as a decimal.
• We work in base 10 decimals and do exact division.
• No rounding is required if the decimal terminates.

Concept / Approach:
To convert a fraction to a decimal, we divide the numerator by the denominator using long division or known fraction to decimal pairs. Here the numerator is 1 and the denominator is 8, so we compute 1 / 8. Since 8 does not divide 1 directly, we introduce decimal places and treat 1.000 as the dividend. This is a standard method for fraction to decimal conversion.

Step-by-Step Solution:
Step 1: Write the fraction as division: 1/8 means 1 divided by 8. Step 2: Since 8 does not go into 1, write 1.000 and perform division with decimals. Step 3: 8 goes into 10 one time, so the first decimal digit is 1 and the remainder is 10 - 8 = 2. Step 4: Bring down the next 0 to get 20. Now 8 goes into 20 two times, remainder 20 - 16 = 4. The next digit is 2. Step 5: Bring down another 0 to get 40. Now 8 goes into 40 five times, remainder 40 - 40 = 0, so the next digit is 5. Step 6: The division ends with zero remainder, so 1/8 = 0.125 exactly.

Verification / Alternative check:
We can quickly verify the result by multiplying back. If 1/8 = 0.125 is correct, then 0.125 * 8 should give 1. Compute 0.125 * 8 = 1.000, which matches the original numerator. Therefore the decimal 0.125 is correct and exact. We can also recall a standard table of common fractions, where 1/2 = 0.5, 1/4 = 0.25, and 1/8 = 0.125.

Why Other Options Are Wrong:
0.225 is greater than 0.2 and would correspond to 9/40, not 1/8.
0.325 is larger still and does not equal 1/8 when multiplied by 8.
0.425 is even larger and clearly does not give 1 when multiplied by 8.

Common Pitfalls:
Students sometimes guess values like 0.25 or 0.2 because they remember related fractions such as 1/4 or 1/5. Another common mistake is to stop the long division too early or to misplace the decimal point, which leads to incorrect results. Remember that 1/8 is smaller than 1/4, so its decimal must be smaller than 0.25. Careful step-by-step division avoids these errors.

Final Answer:
The decimal representation of the fraction 1/8 is 0.125.