When the decimal 0.75 is written as a vulgar fraction in its simplest form, what is that fraction?

Introduction:
This problem asks you to convert a terminating decimal into a vulgar fraction (ordinary fraction) in simplest form. Converting between decimals and fractions is an essential numerical skill used in percentages, ratios, and many quantitative aptitude questions.

Given Data / Assumptions:

• Decimal given: 0.75
• We need the equivalent fraction.
• The answer should be in lowest terms.

Concept / Approach:
A decimal like 0.75 can be written as a fraction by reading it as seventy five hundredths, which is 75/100. After that, we reduce the fraction by dividing numerator and denominator by their greatest common divisor. Since 0.75 is a terminating decimal, this process is straightforward.

Step-by-Step Solution:
Step 1: Write 0.75 as a fraction: 0.75 = 75/100.Step 2: Find the greatest common divisor of 75 and 100.Step 3: Both numbers are divisible by 25: 75 = 25 * 3 and 100 = 25 * 4.Step 4: Divide numerator and denominator by 25.Step 5: Numerator: 75 / 25 = 3.Step 6: Denominator: 100 / 25 = 4.Step 7: Therefore, 0.75 = 3/4 in simplest form.

Verification / Alternative check:
Convert 3/4 back to decimal: 3 ÷ 4 = 0.75. This confirms that 3/4 is indeed the correct fraction for 0.75. No further simplification is possible because 3 and 4 have no common factor greater than 1.

Why Other Options Are Wrong:
3/5 is 0.6, which is less than 0.75. 3/2 equals 1.5, which is greater than 0.75. 3/7 is about 0.4286, and 1/4 is 0.25; both differ significantly from 0.75. Only 3/4 matches the decimal 0.75 exactly.

Common Pitfalls:
Students sometimes misread 0.75 as 75/1000 or confuse it with 0.7 or 0.8. Another frequent error is to stop simplifying at 75/100 and forget to reduce it. Always remember to divide by the greatest common divisor to obtain a fraction in its lowest terms.

Final Answer:
The decimal 0.75 written as a vulgar fraction in simplest form is 3/4.