Write 7.25% as a fraction in simplest form

Write 7.25% as a fraction in simplest form

The Correct Answer and Explanation is:

Correct Answer:

7.25% = 29/400 (in simplest form)

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Explanation

To convert 7.25% into a fraction in simplest form, we follow a series of clear steps involving understanding percentages, decimals, and simplification of fractions.

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Step 1: Understand the meaning of percent

The word percent means “per hundred”. So, 7.25% literally means 7.25 out of 100, or: 7.25%=7.251007.25\% = \frac{7.25}{100}

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Step 2: Eliminate the decimal

We now have a decimal in the numerator: 7.25. To eliminate the decimal, we multiply both the numerator and denominator by 100, since there are two decimal places in 7.25: 7.25100=7.25×100100×100=72510,000\frac{7.25}{100} = \frac{7.25 \times 100}{100 \times 100} = \frac{725}{10,000}

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Step 3: Simplify the fraction

Now we simplify the fraction 725/10,000. To do this, find the greatest common divisor (GCD) of 725 and 10,000.

We can start by dividing both numbers by 25:

• 725 ÷ 25 = 29
• 10,000 ÷ 25 = 400

So: 72510,000=29400\frac{725}{10,000} = \frac{29}{400}

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Step 4: Confirm simplest form

29 is a prime number, and 400 is not divisible by 29. That means 29/400 is already in simplest form.

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Final Answer:

7.25%=294007.25\% = \boxed{\frac{29}{400}}

This fraction represents the same value as 7.25% and cannot be reduced any further. This conversion process is essential for understanding percentages in practical applications such as finance, statistics, and everyday calculations.