Which of the following is the decimal form of 87.5%?
A.
8,750
B.
875
C.
8.75
D.
0.875
The Correct answer and Explanation is: The correct answer is D. 0.875.
Explanation:
To convert a percentage into its decimal form, the general rule is to divide the percentage by 100. This process essentially shifts the decimal point two places to the left. For example, if you have a percentage such as 50%, it is equivalent to 50/100, which equals 0.50 as a decimal.
Now, let’s apply this rule to the given problem:
Step 1: Identify the percentage.
Here, the percentage is 87.5%.
Step 2: Divide the percentage by 100 to convert it into decimal form.
87.5÷100=0.87587.5 \div 100 = 0.87587.5÷100=0.875
So, 87.5% as a decimal is 0.875.
Understanding Why
To understand this further, consider the mathematical basis for converting a percentage to a decimal. A percentage is essentially a ratio that represents a number out of 100. For example, 50% means 50 out of 100, which mathematically translates to 50/100 or 0.50. Similarly, 87.5% means 87.5 out of 100, which is 87.5/100 or 0.875.
Another way to think about it is by imagining the percentage as being multiplied by 1/100. When you multiply 87.5 by 1/100, the result is 0.875, the decimal equivalent.
Common Mistakes
It’s important to avoid common errors when converting percentages to decimals. For example:
- Confusing percentages with whole numbers: Sometimes, people mistakenly treat percentages as if they don’t need to be divided by 100. For instance, incorrectly thinking 87.5% equals 875 (as in option B) is a common mistake.
- Incorrectly placing the decimal point: Some may accidentally shift the decimal point too far or not far enough, leading to incorrect answers like 8.75 or 8,750.
Conclusion
Converting percentages to decimals is a fundamental mathematical skill. Remember, shifting the decimal point two places to the left is key when dividing by 100. Therefore, 87.5% correctly converts to 0.875 in decimal form, making option D the correct choice.