By how much is the decimal number 0.127 greater than the fraction 1/8?

Introduction / Context:
This problem combines decimal and fraction arithmetic. You need to compare a decimal value with a fraction and express their difference as another fraction. This is useful in accuracy analysis and error calculations where small differences are often expressed as fractions.

Given Data / Assumptions:

• Decimal given: 0.127.
• Fraction for comparison: 1/8.
• We must find 0.127 − 1/8 and express the result as a fraction in simplest form.

Concept / Approach:
We can either convert the fraction 1/8 to a decimal and subtract, or convert the decimal 0.127 to a fraction and subtract fractions. Since 1/8 has a known decimal 0.125, comparing 0.127 and 0.125 is straightforward. The difference can then be written as a decimal and further converted to a fraction by recognizing its place value.

Step-by-Step Solution:
Step 1: Convert 1/8 to decimal. From earlier questions, 1/8 = 0.125. Step 2: Compute the difference between the decimals: 0.127 − 0.125. Step 3: Subtraction gives 0.002. Step 4: Now express 0.002 as a fraction. There are three decimal places, so 0.002 = 2/1000. Step 5: Simplify 2/1000 by dividing numerator and denominator by 2, obtaining 1/500. Step 6: Therefore, 0.127 is greater than 1/8 by 1/500.

Verification / Alternative check:
We can confirm by converting 1/500 back to decimal. 1/500 equals 0.002 because 1 divided by 500 can be written as 2 divided by 1000. Adding this difference to 0.125 gives 0.125 + 0.002 = 0.127, which matches the given decimal. Thus, the fractional difference 1/500 is correct.

Why Other Options Are Wrong:
1/100 equals 0.01, which is much larger than the small difference of 0.002.
1/1500 is approximately 0.000666, which is smaller than 0.002 and does not match the difference.
1/2 equals 0.5, which is far too large and clearly incorrect in this context.

Common Pitfalls:
A common error is misplacing the decimal when subtracting 0.127 and 0.125 and getting 0.012 or 0.02. Another pitfall is writing 0.002 as 2/100 or 1/50, which misrepresents the place value. Always count the number of decimal digits to write the correct power of 10 in the denominator and then reduce the fraction carefully.

Final Answer:
The number 0.127 is greater than 1/8 by 1/500.