Convert Fraction to Percentage: Express 215/645 as a Percentage

Q: What does the repeating decimal 0.3333... actually mean?

The repeating decimal $ 0.\overline{3} $ means the 3's go on forever! This equals exactly $ \frac{1}{3} $, so never round it - express it as the mixed number percentage instead.

Q: How do I know when to use a mixed number percentage?

Use mixed number percentages when you get a repeating decimal that represents a simple fraction. Common ones: $ 0.\overline{3} = 33\frac{1}{3}\% $ and $ 0.\overline{6} = 66\frac{2}{3}\% $.

Q: Can I simplify the fraction 215/645 before converting?

Yes! Always check if you can simplify first. $ \frac{215}{645} = \frac{1}{3} $ after dividing both by 215. This makes the conversion much easier!

Q: Why is 33.33% different from 33⅓%?

$ 33.33\% $ is an approximation, while $ 33\frac{1}{3}\% $ is the exact answer. The exact form shows the true mathematical relationship without any rounding error.

Q: What if my calculator shows a long decimal?

Look for patterns in the decimal! If you see repeating digits like 0.333333..., recognize this as $ \frac{1}{3} $ and convert to the mixed number percentage form.

Fraction to Percentage with Repeating Decimals

What is 215 over 645 expressed as a percentage?

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Step-by-step video solution

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00:05 Let's find what percentage 215 is of 645.

00:11 First, we'll use the percentage formula.

00:15 Divide 215 by 645, then multiply by 100.

00:22 Look for factors of 645. We have 215 times 3.

00:28 Simplify the fraction if you can.

00:34 Great job! That's how we solve it.

Step-by-step written solution

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Understand the problem

What is 215 over 645 expressed as a percentage?

Step-by-step solution

To express $\frac{215}{645}$ as a percentage, we follow these steps:

Step 1: Divide the numerator by the denominator. $\frac{215}{645} = 0.3333333333\ldots$ The result is an approximation of the repeating decimal $0.3333\ldots$ .
Step 2: Multiply the decimal result from Step 1 by 100 to convert it to a percentage. $0.3333\ldots \times 100 = 33.3333\ldots$ As a percentage, this can be expressed as $33\frac{1}{3}\%$ .

Therefore, the percentage representation of $\frac{215}{645}$ is $33\frac{1}{3}\%$ .

Final Answer

$33\frac{1}{3}\%$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Divide numerator by denominator to get decimal form
Technique: Multiply decimal by 100: $0.\overline{3} \times 100 = 33.\overline{3}\%$
Check: Convert back: $33\frac{1}{3}\% = \frac{1}{3} = 0.\overline{3}$ ✓

Common Mistakes

Avoid these frequent errors

Rounding the decimal too early
Don't round 0.3333... to 0.33 and get 33% = wrong answer! This loses the repeating pattern and gives an incorrect percentage. Always recognize $0.\overline{3} = \frac{1}{3}$ and express as $33\frac{1}{3}\%$ .

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

What does the repeating decimal 0.3333... actually mean?

The repeating decimal $0.\overline{3}$ means the 3's go on forever! This equals exactly $\frac{1}{3}$ , so never round it - express it as the mixed number percentage instead.

How do I know when to use a mixed number percentage?

Use mixed number percentages when you get a repeating decimal that represents a simple fraction. Common ones: $0.\overline{3} = 33\frac{1}{3}\%$ and $0.\overline{6} = 66\frac{2}{3}\%$ .

Can I simplify the fraction 215/645 before converting?

Yes! Always check if you can simplify first. $\frac{215}{645} = \frac{1}{3}$ after dividing both by 215. This makes the conversion much easier!

Why is 33.33% different from 33⅓%?

$33.33\%$ is an approximation, while $33\frac{1}{3}\%$ is the exact answer. The exact form shows the true mathematical relationship without any rounding error.

What if my calculator shows a long decimal?

Look for patterns in the decimal! If you see repeating digits like 0.333333..., recognize this as $\frac{1}{3}$ and convert to the mixed number percentage form.

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