Difficulty: Easy
Correct Answer: 1/500
Explanation:
Introduction:
This question measures your skill in comparing a decimal with a fraction and finding their difference as a fraction. It is a typical type of problem in decimal–fraction conversion and comparison topics in quantitative aptitude.
Given Data / Assumptions:
Concept / Approach:
To find how much greater one number is than another, we subtract the smaller from the larger. So we calculate 0.127 − 1/8. It is convenient to convert both numbers to decimals or both to fractions. Since 0.127 is already a decimal, we can convert it to a fraction and subtract 1/8 in fractional form.
Step-by-Step Solution:
Step 1: Convert 1/8 to a decimal or leave it as a fraction. 1/8 = 0.125.Step 2: Compare 0.127 and 0.125; clearly, 0.127 is larger.Step 3: Compute the decimal difference: 0.127 − 0.125 = 0.002.Step 4: Now express 0.002 as a fraction. 0.002 = 2/1000.Step 5: Simplify 2/1000 by dividing numerator and denominator by 2: 2/1000 = 1/500.Step 6: Therefore, 0.127 is greater than 1/8 by 1/500.
Verification / Alternative check:
Convert 1/500 back to decimal: 1 ÷ 500 = 0.002. Note that 1/8 = 0.125. Adding 0.002 to 0.125 gives 0.127, which confirms that the difference is indeed 1/500.
Why Other Options Are Wrong:
1/100 equals 0.01, which is too large. 1/1500 equals approximately 0.000666..., much smaller than 0.002. 1/2 equals 0.5, clearly unrelated to this small difference. 1/200 equals 0.005, also too large. Only 1/500 corresponds to the precise difference of 0.002 between 0.127 and 0.125.
Common Pitfalls:
Students sometimes subtract 1/8 from 0.127 incorrectly due to decimal misalignment or confuse which number is larger. Others may convert the fraction to an imprecise decimal and then round too early. Keeping a few decimal places and doing exact subtraction, or using fraction forms from the start, ensures accuracy.
Final Answer:
The number 0.127 is greater than 1/8 by 1/500.
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