What is the decimal representation of the fraction 3/8, written as an exact terminating decimal?

Introduction / Context:
This question again deals with converting a fraction to its decimal form. The fraction 3/8 is common in measurement and probability problems, and knowing its decimal value helps speed up many calculations.

Given Data / Assumptions:

• Fraction: 3/8.
• We need its decimal representation.
• Standard base 10 decimals are used, and the answer is exact.

Concept / Approach:
We already know that 1/8 = 0.125 from earlier questions. Since 3/8 is three times 1/8, we can multiply 0.125 by 3 to get the decimal value. Alternatively, we can perform the long division 3 ÷ 8 directly.

Step-by-Step Solution:
Step 1: Recall that 1/8 = 0.125. Step 2: Use the relation 3/8 = 3 × (1/8). Step 3: Multiply 0.125 by 3. Step 4: 0.125 × 3 = 0.375 because 125 × 3 = 375 and we keep three decimal places. Step 5: Therefore 3/8 = 0.375.

Verification / Alternative check:
As a check, perform the division 3 ÷ 8. When we divide 3.000 by 8, we get 0.3 with remainder 3 * 10 − 8 * 3 = 4, then 8 goes into 40 five times. The process yields 0.375 exactly. This confirms that the decimal representation of 3/8 is 0.375.

Why Other Options Are Wrong:
0.247 is smaller than 0.3 and does not correspond to three eighths.
0.214 is also much smaller and would correspond to a very different fraction.
0.125 is the decimal for 1/8, not for 3/8.

Common Pitfalls:
Some learners confuse 3/8 with 1/4 or 1/3 and choose 0.25 or 0.333. Others may multiply incorrectly when using 1/8 = 0.125. Always verify by multiplication or direct division if you are not fully sure of the standard fraction to decimal pairs.

Final Answer:
The decimal representation of 3/8 is 0.375.