Express the terminating decimals 0.875 and 0.375 each as vulgar fractions in their simplest form.

Introduction:
This problem checks whether you can convert two terminating decimals, 0.875 and 0.375, into their equivalent fractional forms. Working comfortably between decimals and fractions is important in percentages, ratios, and many aptitude questions.

Given Data / Assumptions:

• Decimals: 0.875 and 0.375.
• We must write each decimal as a fraction.
• Each fraction should be in simplest form.

Concept / Approach:
To convert a decimal to a fraction, write the decimal as an integer divided by a power of 10 (for example, 1000 if there are three decimal places) and then simplify. Terminating decimals always lead to fractions with denominators that involve powers of 2 and 5. We simplify by dividing numerator and denominator by their greatest common divisor.

Step-by-Step Solution:
Step 1: Convert 0.875 to a fraction. It has three decimal places, so write 0.875 = 875/1000.Step 2: Find the greatest common divisor of 875 and 1000. Both are divisible by 125: 875 = 125 * 7 and 1000 = 125 * 8.Step 3: Divide numerator and denominator by 125: 875/1000 = 7/8.Step 4: Convert 0.375 to a fraction: 0.375 = 375/1000.Step 5: Find the greatest common divisor of 375 and 1000. Both are divisible by 125: 375 = 125 * 3 and 1000 = 125 * 8.Step 6: Divide numerator and denominator by 125: 375/1000 = 3/8.Step 7: So 0.875 = 7/8 and 0.375 = 3/8.

Verification / Alternative check:
Convert back to decimals: 7/8 = 0.875 and 3/8 = 0.375. Both match the original decimals exactly, confirming that the conversions are correct and fully simplified.

Why Other Options Are Wrong:
The pairs 3/11 and 7/11, 7/9 and 9/13, and 7/9 and 9/11 give decimals that do not equal 0.875 or 0.375. The option 5/8 and 3/8 gives correct value for 0.375 (3/8) but 5/8 is 0.625, not 0.875. Only the pair 7/8 and 3/8 matches both decimals correctly.

Common Pitfalls:
Some learners simplify only partially or guess fractions without converting properly. Others may miscount decimal places and write, for example, 0.875 as 875/100 instead of 875/1000. Always match the number of decimal places to the correct power of 10 and then reduce the fraction by dividing by the greatest common divisor.

Final Answer:
The correct fractional forms are 0.875 = 7/8 and 0.375 = 3/8.