Difficulty: Easy
Correct Answer: 0.375
Explanation:
Introduction / Context:This question checks your understanding of how to convert a simple fraction into its decimal form. Converting between fractions and decimals is a very common skill used in aptitude tests, data interpretation and everyday calculations such as money, measurements and percentages.
Given Data / Assumptions:
Concept / Approach:To convert a fraction to a decimal, we divide the numerator by the denominator. Here we compute 3 ÷ 8. Because 8 is a factor of 2^3, the decimal will terminate, not repeat. We can use long division or use the idea of equivalent fractions with a denominator that is a power of 10.
Step-by-Step Solution:
Step 1: Write the division 3 ÷ 8.Step 2: Because 3 is less than 8, write it as 3.000 and divide by 8.Step 3: 8 goes into 30 three times (3 * 8 = 24). Remainder = 30 - 24 = 6.Step 4: Bring down another 0 to make 60. 8 goes into 60 seven times (7 * 8 = 56). Remainder = 60 - 56 = 4.Step 5: Bring down another 0 to make 40. 8 goes into 40 exactly five times (5 * 8 = 40). Remainder = 0, so the decimal terminates at 0.375.Verification / Alternative check:Notice that 3/8 = (3 * 125) / (8 * 125) = 375/1000. Writing 375/1000 as a decimal directly gives 0.375. This confirms our long division result.
Why Other Options Are Wrong:1.375 is 11/8, which is larger than 1 and does not match 3/8. 2.375 corresponds to 19/8 and is even larger. 3.75 corresponds to 15/4. All these values are much bigger than 3/8, so they cannot be correct.
Common Pitfalls:A common mistake is to incorrectly stop the division too early or misplace the decimal point, leading to 0.37 or 0.38 instead of the exact 0.375. Another error is to confuse 3/8 with 3.8, which is a completely different number. Always remember that a fraction less than 1 must convert to a decimal less than 1.
Final Answer:The decimal representation of 3/8 is 0.375.
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