Difficulty: Easy
Correct Answer: 3/4
Explanation:
Introduction / Context:
This question checks your ability to convert a simple terminating decimal into an equivalent fraction, sometimes called a vulgar fraction. Converting between decimals and fractions is important in topics like percentages, ratios, and measurement conversions.
Given Data / Assumptions:
Concept / Approach:
A terminating decimal can be written as a fraction whose denominator is a power of 10. After that, we simplify the fraction by dividing numerator and denominator by their greatest common divisor. Here, 0.75 has two decimal places, so it can initially be written over 100 and then reduced.
Step-by-Step Solution:
Step 1: Write 0.75 as a fraction with denominator 100. Since there are two decimal places, 0.75 = 75/100.
Step 2: Find the greatest common divisor of 75 and 100. Both are divisible by 25.
Step 3: Divide numerator and denominator by 25. We get 75 / 25 = 3 and 100 / 25 = 4.
Step 4: Therefore 0.75 = 3/4 in simplest form.
Step 5: Check whether 3 and 4 have any further common factor greater than 1. They do not, so 3/4 is fully simplified.
Verification / Alternative check:
We can verify by converting 3/4 back to a decimal. Compute 3/4 as 3 ÷ 4. Since 4 goes into 3.00 exactly 0.75 times, the decimal equals 0.75. This confirms that the original decimal and the fraction 3/4 represent the same value.
Why Other Options Are Wrong:
3/5 equals 0.6, which is smaller than 0.75.
3/2 equals 1.5, which is greater than 0.75 and is an improper fraction here.
3/7 is approximately 0.4286, also not equal to 0.75.
Common Pitfalls:
Some learners confuse 0.75 with 0.7 or 0.8 and may incorrectly choose 3/5 or another fraction. Others may stop at 75/100 and forget to simplify. Remember that fractions should usually be given in lowest terms unless the question states otherwise.
Final Answer:
The vulgar fraction equal to 0.75 is 3/4.
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