Convert terminating decimal to a simplified fraction: Express 0.34 as a vulgar fraction in lowest terms.
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A18/50
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B16/50
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C17/50
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D19/50
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E34/100
Answer
Correct Answer: 17/50
Explanation
Introduction / Context:Changing a terminating decimal to a common fraction is a foundational skill for algebra and arithmetic. The key is to place the decimal over an appropriate power of 10 and then reduce.
Given Data / Assumptions:
- Decimal: 0.34
- We want the fraction in lowest terms.
Concept / Approach:For two decimal places, write 0.34 as 34/100. Then simplify by dividing numerator and denominator by their greatest common divisor.
Step-by-Step Solution:
0.34 = 34/100Compute gcd of 34 and 100 which is 2Divide: 34/100 = (34 ÷ 2) / (100 ÷ 2) = 17/50Verification / Alternative check:Convert back: 17/50 = 0.34 because 17 ÷ 50 = 0.34 exactly.
Why Other Options Are Wrong:18/50 and 16/50 do not equal 0.34. 19/50 equals 0.38. 34/100 is equivalent but not in lowest terms.
Common Pitfalls:Stopping at 34/100 and forgetting to reduce or dividing by an incorrect common factor.
Final Answer:17/50