Convert the decimal 0.0068 into a vulgar (common) fraction in lowest terms.

Introduction / Context:
This question checks your ability to convert a finite decimal into a common fraction and then reduce that fraction to lowest terms. This is a basic but important skill in number systems and arithmetic.

Given Data / Assumptions:

• Decimal: 0.0068.
• We must convert this decimal into a fraction.
• The fraction should be in simplest form.

Concept / Approach:
To convert a decimal to a fraction, we count the number of decimal places and use a power of 10 as the denominator. Then we simplify the fraction by dividing numerator and denominator by their greatest common divisor.

Step-by-Step Solution:

Verification / Alternative check:
Convert 17/2500 back to a decimal to confirm: 17 ÷ 2500 = 0.0068. This matches the original decimal, confirming that 17/2500 is correct.

Why Other Options Are Wrong:
7/1250 equals 0.0056, not 0.0068. 17/5000 equals 0.0034, which is too small. 7/1750 also simplifies to 1/250 and is 0.004, which does not match the given decimal. None of these alternatives produce 0.0068.

Common Pitfalls:
A common mistake is miscounting the number of decimal places and using 1000 instead of 10000, which leads to an incorrect fraction. Another error is forgetting to simplify the fraction, leaving it as 68/10000 instead of reducing it to lowest terms.

Final Answer:
The decimal 0.0068, written as a vulgar fraction in simplest form, is 17/2500.