Convert 7.5% to a Fraction: Finding the Hundredths Form

Percentage Conversion with Decimal Numerators

Write the percentage 7.5% as a fraction with denominator 100.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's change percentages into fractions, step by step.
00:11 Remember, a percentage is a fraction. The numerator is the percentage number, and the denominator is always one hundred.
00:18 Now, let's apply this rule to the exercise we're working on. Take it one step at a time!
00:32 And that's how you find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Write the percentage 7.5% as a fraction with denominator 100.

2

Step-by-step solution

We use the formula:

x100=x% \frac{x}{100}=x\%

7.5100=7.5% \frac{7.5}{100}=7.5\%

3

Final Answer

7.5100 \frac{7.5}{100}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Any percentage equals that number over 100 as a fraction
  • Technique: Write 7.5% as 7.5100 \frac{7.5}{100} directly from the definition
  • Check: Convert back: 7.5100=7.5÷100=0.075=7.5% \frac{7.5}{100} = 7.5 \div 100 = 0.075 = 7.5\%

Common Mistakes

Avoid these frequent errors
  • Converting decimals to whole numbers in the numerator
    Don't change 7.5% to 75100 \frac{75}{100} = 75%! This multiplies your percentage by 10 and gives a completely wrong answer. Always keep the decimal number exactly as given when using denominator 100.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction \( \frac{7}{100} \) into a percentage.

FAQ

Everything you need to know about this question

Why can I have a decimal in the numerator of a fraction?

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Decimals in numerators are perfectly valid! A fraction like 7.5100 \frac{7.5}{100} just means "7.5 parts out of 100 total parts." It's the most direct way to convert a percentage.

Should I simplify 7.5100 \frac{7.5}{100} to something else?

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The question specifically asks for denominator 100, so 7.5100 \frac{7.5}{100} is your final answer. Don't change it to 751000 \frac{75}{1000} or 340 \frac{3}{40} .

What if I wrote 75100 \frac{75}{100} instead?

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That would equal 75%, not 7.5%! You accidentally multiplied by 10. Remember: 7.5% means 7.5 out of 100, not 75 out of 100.

How do I remember the percentage-to-fraction rule?

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Think of the percent symbol (%) as "out of 100." So 7.5% literally means "7.5 out of 100" which is 7.5100 \frac{7.5}{100} !

Can I check my answer by converting back to a percentage?

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Yes! Divide the numerator by denominator: 7.5÷100=0.075 7.5 \div 100 = 0.075 . Then multiply by 100: 0.075×100=7.5% 0.075 \times 100 = 7.5\%

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