Have you ever come across a percentage and wondered how it can be expressed as a fraction?Converting a percentage to a fraction might seem daunting at first, but with the right steps, it becomes a straightforward process. In this article, we will guide you through the step-by-step process of converting a percentage to a fraction, answering some common questions along the way.

What is a percentage?

A percentage is a number expressing a proportion out of 100. It is denoted by the symbol “%”.

Why would I want to convert a percentage to a fraction?

Converting a percentage to a fraction allows you to express a proportion in a different format. Fractions are often more useful when dealing with mathematical operations or comparisons.

Now let’s dive into the step-by-step process of converting a percentage to a fraction.

Step 1: Express the percentage as a decimal
To begin, you need to convert the percentage to a decimal. This can be done by dividing the percentage value by 100. For example, if you have 75%, divide it by 100 to get 0.75.

Step 2: Write the decimal as a fraction
The next step involves writing the decimal as a fraction. To do this, you need to identify the place value of the last digit after the decimal point. If the decimal has one digit after the decimal point, the fraction will have 10 as the denominator. If it has two digits, the denominator will be 100, and so on. For example, if your decimal is 0.75, you can write it as 75/100.

Step 3: Simplify the fraction
Once you have the fraction, it is essential to simplify it to its lowest terms. You can do this by dividing both the numerator and the denominator by their greatest common divisor (GCD). In our example, the GCD of 75 and 100 is 25. So, dividing both by 25, we get 3/4.

Congratulations! You have successfully converted a percentage to a fraction. Remember to simplify the fraction whenever possible.

What if the decimal has more than two digits?

If your decimal has three digits after the decimal point, the denominator will be 1,000. Similarly, for four digits, the denominator will be 10,000, and so on. The process remains the same; write the decimal as the numerator and use the appropriate denominator.

Can a percentage with a decimal also be converted?

Yes, a percentage with a decimal can be converted just like any other percentage. First, express the decimal as a percentage by multiplying by 100. Then follow the steps mentioned earlier to convert it to a fraction.

It’s important to note that in some cases, the fraction obtained may not be in its simplest form. For instance, if you convert 20%, your fraction would be 20/100. But when simplified, it becomes 1/5.

In conclusion, converting a percentage to a fraction involves a simple step-by-step process. Start by converting the percentage to a decimal, then write it as a fraction, and finally, simplify the fraction. Now that you are equipped with this knowledge, you can confidently convert percentages to fractions and understand mathematical proportions in a new light.

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