Convert Fraction to Percentage: Solving 0.2/100

Q: Is 0.2% the same as 2%?

No! 0.2% is much smaller than 2%. As decimals: 0.2% = 0.002 while 2% = 0.02. The decimal point position matters greatly!

Q: How do I know if my percentage makes sense?

Check if your percentage is reasonable. Since $ \frac{0.2}{100} $ is less than 1, the percentage should be less than 100%. 0.2% makes sense!

Q: What if I got 20% as my answer?

That's a common error! You might have calculated $ 0.2 \times 100 = 20\% $ instead of $ \frac{0.2}{100} \times 100 = 0.2\% $. Always divide first, then multiply by 100.

Q: Can I convert this to a simpler fraction first?

Yes! $ \frac{0.2}{100} = \frac{2}{1000} = \frac{1}{500} $. Then $ \frac{1}{500} \times 100 = \frac{100}{500} = 0.2\% $. Same result!

Fraction Percentage Conversion with Small Decimals

Convert the fraction into a percentage:

$\frac{0.2}{100}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's learn how to convert fractions into percentages!

00:11 If a fraction has one hundred as the denominator, the numerator is the same as the percentage. For example, X over One Hundred is X percent.

00:23 Now, let's apply this rule to our exercise.

00:27 And here is the solution! You've got this.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert the fraction into a percentage:

$\frac{0.2}{100}=\text{?}$

Step-by-step solution

The task is to convert the fraction $\frac{0.2}{100}$ into a percentage.

To convert a fraction to a percentage, we follow this process:

Step 1: Identify the numerator and the denominator. Here, the numerator is $0.2$ and the denominator is $100$ .
Step 2: Use the formula for percentage conversion: $\text{Percentage} = \left(\frac{\text{Numerator}}{\text{Denominator}}\right) \times 100$ .
Step 3: Apply the values from the fraction: $\left(\frac{0.2}{100}\right) \times 100$ .
Step 4: Calculate the result: $0.2 \times 1 = 0.2$ .

The conversion of the given fraction to a percentage is $0.2\%$ . Therefore, the correct answer is \textbf{0.2\%}.

Final Answer

0.2%

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply fraction by 100 to get percentage
Technique: $\frac{0.2}{100} \times 100 = 0.2$ then add % symbol
Check: Convert back: 0.2% = 0.2/100 = 0.002 as decimal ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100 when converting
Don't just write 0.2/100 as 0.002% = wrong answer! This skips the multiplication step needed for percentage conversion. Always multiply the decimal result by 100: (0.2/100) × 100 = 0.2%.

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 multiply by 100 if the denominator is already 100?

The denominator being 100 doesn't mean it's already a percentage! To convert any fraction to a percentage, you must multiply by 100. Here: $\frac{0.2}{100} \times 100 = 0.2\%$ .

Is 0.2% the same as 2%?

No! 0.2% is much smaller than 2%. As decimals: 0.2% = 0.002 while 2% = 0.02. The decimal point position matters greatly!

How do I know if my percentage makes sense?

Check if your percentage is reasonable. Since $\frac{0.2}{100}$ is less than 1, the percentage should be less than 100%. 0.2% makes sense!

What if I got 20% as my answer?

That's a common error! You might have calculated $0.2 \times 100 = 20\%$ instead of $\frac{0.2}{100} \times 100 = 0.2\%$ . Always divide first, then multiply by 100.

Can I convert this to a simpler fraction first?

Yes! $\frac{0.2}{100} = \frac{2}{1000} = \frac{1}{500}$ . Then $\frac{1}{500} \times 100 = \frac{100}{500} = 0.2\%$ . Same result!

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