Convert 10.5% to a Fraction with Denominator 100: Step-by-Step

Q: Why do I keep the decimal 10.5 in the numerator?

The decimal 10.5 represents the exact percentage value. Changing it to 10 or 11 would give you a different percentage entirely! Keep decimals exactly as given.

Q: Is having a decimal in the numerator okay?

Absolutely! Fractions can have decimals in the numerator. The fraction $ \frac{10.5}{100} $ is perfectly valid and correct.

Q: How do I convert this back to check my work?

Divide the numerator by denominator: $ 10.5 \div 100 = 0.105 $. Then multiply by 100%: 0.105 × 100% = 10.5% ✓

Q: What if the percentage was 10.75% instead?

Same process! You'd write $ \frac{10.75}{100} $. The numerator always matches the number before the % symbol, decimal and all.

Percentage Conversion with Decimal Numerators

Write the percentage 10.5% as a fraction with a denominator of 100.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's convert percentages into fractions.

00:11 Picture a fraction, where the top number, or numerator, is the percentage, X. And the bottom number, or denominator, is one hundred.

00:19 Now, let's apply this formula to our exercise.

00:26 And here we have the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the percentage 10.5% as a fraction with a denominator of 100.

Step-by-step solution

To solve this problem, we need to convert the percentage 10.5% into a fraction with a denominator of 100. We proceed as follows:

Step 1: Recognize that the formula for converting a percentage to a fraction involves placing the percentage number over 100. This is because a percentage is already a number out of 100.

Step 2: Apply the formula to convert 10.5% into a fraction:
We write 10.5% as $\frac{10.5}{100}$ .

Step 3: Verify the result: The fraction $\frac{10.5}{100}$ indeed has a denominator of 100, meeting the requirements specified in the problem.

Therefore, the percentage 10.5% expressed as a fraction with a denominator of 100 is $\frac{10.5}{100}$ .

Final Answer

$\frac{10.5}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place percentage value over 100 to create fraction
Technique: Keep decimal intact: 10.5% becomes $\frac{10.5}{100}$
Check: Denominator equals 100 and numerator matches percentage value ✓

Common Mistakes

Avoid these frequent errors

Rounding 10.5 to 10 or 11
Don't round 10.5% to 10% and write $\frac{10}{100}$ = wrong value! This changes the percentage completely from 10.5% to 10%. Always keep the exact decimal value 10.5 in the numerator.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do I keep the decimal 10.5 in the numerator?

The decimal 10.5 represents the exact percentage value. Changing it to 10 or 11 would give you a different percentage entirely! Keep decimals exactly as given.

Can I simplify this fraction further?

You could multiply both numerator and denominator by 10 to get $\frac{105}{1000}$ , but the problem specifically asks for denominator 100. Always follow the exact requirements!

Is having a decimal in the numerator okay?

Absolutely! Fractions can have decimals in the numerator. The fraction $\frac{10.5}{100}$ is perfectly valid and correct.

How do I convert this back to check my work?

Divide the numerator by denominator: $10.5 \div 100 = 0.105$ . Then multiply by 100%: 0.105 × 100% = 10.5% ✓

What if the percentage was 10.75% instead?

Same process! You'd write $\frac{10.75}{100}$ . The numerator always matches the number before the % symbol, decimal and all.

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