When the fraction 3/8 is converted to a decimal number, what is its value?

Introduction:
This problem simply asks you to convert the fraction 3/8 into its decimal equivalent. Mastering fraction to decimal conversion is essential for working with percentages, ratios, and many other numerical questions in aptitude tests.

Given Data / Assumptions:

• Fraction: 3/8.
• We must express it as a decimal.
• We want the exact terminating decimal.

Concept / Approach:
To convert a fraction to a decimal, perform the division of numerator by denominator. Because 8 is a power of 2, we know the decimal will terminate. Alternatively, we can express 3/8 with a denominator that is a power of 10 and then read off the decimal representation.

Step-by-Step Solution:
Step 1: Interpret 3/8 as 3 ÷ 8.Step 2: Perform the division using long division or mental math. 8 does not go into 3, so consider 30 tenths.Step 3: 8 goes into 30 three times (3 * 8 = 24), remainder 6. Bring down a 0 to make 60.Step 4: 8 goes into 60 seven times (7 * 8 = 56), remainder 4. Bring down a 0 to make 40.Step 5: 8 goes into 40 five times (5 * 8 = 40), remainder 0.Step 6: Therefore, the quotient is 0.375.

Verification / Alternative check:
We can express 3/8 with denominator 1000: multiply numerator and denominator by 125: (3 * 125)/(8 * 125) = 375/1000. Writing 375/1000 as a decimal gives 0.375, confirming our long division result.

Why Other Options Are Wrong:
1.375 and 2.375 are larger than 1 and would require a numerator greater than the denominator. 3.75 is ten times the correct value and corresponds to 30/8, not 3/8. 0.735 is just a rearrangement of the digits and does not match the correct decimal of 3/8. Only 0.375 equals 3/8 exactly.

Common Pitfalls:
Students may misplace the decimal point or stop the division too early, leading to partial or incorrect results like 0.37. Others confuse 3/8 with 3/10 or 1/8. Knowing a few common equivalents, such as 1/8 = 0.125 and 3/8 = 0.375, can save time.

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