Convert Fraction 13/10000 to Percentage: Step-by-Step Solution

Q: Why is the percentage so small (0.13%)?

The fraction $ \frac{13}{10000} $ represents 13 parts out of 10,000, which is a very small portion! When you convert small fractions to percentages, you naturally get small percentage values.

Q: Can I just move the decimal point instead of multiplying by 100?

Yes! Moving the decimal point two places to the right is the same as multiplying by 100. So 0.0013 becomes 0.13%.

Q: How do I know which decimal place to look at?

First convert the fraction to decimal: $ \frac{13}{10000} = 0.0013 $. Then multiply by 100 (or move decimal right 2 places) to get 0.13%.

Q: What if I got 13% as my answer?

You likely forgot about the large denominator! $ \frac{13}{100} = 13\% $, but $ \frac{13}{10000} $ has 100 times more in the denominator, making it 100 times smaller.

Q: Is there a shortcut for fractions with denominators like 10000?

Yes! Since 10000 = 10² × 100, you can write $ \frac{13}{10000} = \frac{13}{100} \times \frac{1}{100} = 13\% \times \frac{1}{100} = 0.13\% $.

Fraction to Percentage with Small Decimal Values

Write the fraction $\frac{13}{10000}$ as a percentage

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's convert fractions into percentages.

00:10 Simply multiply the fraction by 100 to change it into a percentage.

00:23 Next, break down 10-thousand into two factors of 100.

00:27 Try to simplify it whenever possible.

00:35 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Write the fraction $\frac{13}{10000}$ as a percentage

Step-by-step solution

To convert the fraction $\frac{13}{10000}$ into a percentage, we follow these steps:

Step 1: Identify the given fraction, which is $\frac{13}{10000}$ .
Step 2: The goal is to express this fraction as a percentage. According to the formula, we multiply the fraction by 100 to find its percentage equivalent.
Step 3: Perform the multiplication: $\frac{13}{10000} \times 100 = \frac{13 \times 100}{10000} = \frac{1300}{10000}$
Step 4: Simplify the result: $\frac{1300}{10000} = 0.13$ This gives us the percentage value.

Therefore, the fraction $\frac{13}{10000}$ is equivalent to $0.13\%$ in percentage form.

The correct choice from the given options is $0.13\%$ .

Final Answer

0.13%

Key Points to Remember

Essential concepts to master this topic

Formula: Multiply fraction by 100 to get percentage
Technique: $\frac{13}{10000} \times 100 = \frac{1300}{10000} = 0.13\%$
Check: Convert back: 0.13% ÷ 100 = 0.0013 = $\frac{13}{10000}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to include the % symbol
Don't just write 0.13 as your final answer = incomplete solution! The decimal 0.13 means thirteen hundredths, but 0.13% means thirteen thousandths of a percent. Always include the % symbol when converting to percentage form.

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 is the percentage so small (0.13%)?

The fraction $\frac{13}{10000}$ represents 13 parts out of 10,000, which is a very small portion! When you convert small fractions to percentages, you naturally get small percentage values.

Can I just move the decimal point instead of multiplying by 100?

Yes! Moving the decimal point two places to the right is the same as multiplying by 100. So 0.0013 becomes 0.13%.

How do I know which decimal place to look at?

First convert the fraction to decimal: $\frac{13}{10000} = 0.0013$ . Then multiply by 100 (or move decimal right 2 places) to get 0.13%.

What if I got 13% as my answer?

You likely forgot about the large denominator! $\frac{13}{100} = 13\%$ , but $\frac{13}{10000}$ has 100 times more in the denominator, making it 100 times smaller.

Is there a shortcut for fractions with denominators like 10000?

Yes! Since 10000 = 10² × 100, you can write $\frac{13}{10000} = \frac{13}{100} \times \frac{1}{100} = 13\% \times \frac{1}{100} = 0.13\%$ .

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