Convert 5.2 Out of 10 into a Percentage: A Step-by-Step Guide

Q: Why do I multiply by 100 to get a percentage?

Percentage means "per hundred", so you're converting to parts out of 100. When you multiply $ \frac{5.2}{10} \times 100 $, you're finding how many parts out of 100 this represents.

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

Yes! Moving the decimal point two places to the right is the same as multiplying by 100. So 0.52 becomes 52%. This shortcut works perfectly for decimal-to-percentage conversions.

Q: What if my fraction doesn't have 10 in the denominator?

The same rule applies! For any fraction like $ \frac{3}{4} $, just multiply by 100: $ \frac{3}{4} \times 100 = 75% $. The denominator doesn't matter.

Q: How do I know if 52% makes sense for this problem?

Think logically: $ \frac{5.2}{10} $ means 5.2 out of 10 parts. Since 5.2 is slightly more than half of 10, the percentage should be slightly more than 50%. 52% fits perfectly!

Q: What's the difference between 0.52 and 52%?

They represent the same value but in different forms! 0.52 is the decimal form and 52% is the percentage form. Always include the % symbol when expressing as a percentage.

Decimal Fractions with Percentage Conversion

Convert the following fraction into a percentage:

$\frac{5.2}{10}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert fractions to percentages

00:05 A fraction with a denominator equal to 100 equals the numerator in percentage form (X)

00:12 Apply this formula to our exercise

00:17 Multiply both the numerator and denominator by 10 to obtain a denominator equal to 100

00:32 Proceed to calculate

00:42 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert the following fraction into a percentage:

$\frac{5.2}{10}=\text{?}$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given fraction $\frac{5.2}{10}$ .
Step 2: Apply the formula for converting a fraction to a percentage.
Step 3: Perform the necessary calculation to find the percentage.

Now, let's work through each step:

Step 1: The problem gives us the fraction $\frac{5.2}{10}$ .

Step 2: We use the conversion formula:

$\text{Percentage} = \left(\frac{5.2}{10}\right) \times 100\%$

Step 3: Plugging in our values, we multiply:

$\left(\frac{5.2}{10}\right) \times 100 = 0.52 \times 100 = 52$

Therefore, the fraction $\frac{5.2}{10}$ is equivalent to $52\%$ .

This corresponds to choice 3, which is 52%.

Final Answer

52%

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply any fraction by 100% to convert to percentage
Technique: Calculate $\frac{5.2}{10} \times 100 = 0.52 \times 100 = 52$
Check: Verify 52% equals 0.52 as decimal: 52 ÷ 100 = 0.52 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100 when converting
Don't just calculate $\frac{5.2}{10} = 0.52$ and stop there = wrong answer of 0.52 instead of 52%! The decimal 0.52 is not the same as the percentage. Always multiply by 100 to complete the percentage conversion.

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 to get a percentage?

Percentage means "per hundred", so you're converting to parts out of 100. When you multiply $\frac{5.2}{10} \times 100$ , you're finding how many parts out of 100 this represents.

Can I just move the decimal point instead of multiplying?

Yes! Moving the decimal point two places to the right is the same as multiplying by 100. So 0.52 becomes 52%. This shortcut works perfectly for decimal-to-percentage conversions.

What if my fraction doesn't have 10 in the denominator?

The same rule applies! For any fraction like $\frac{3}{4}$ , just multiply by 100: $\frac{3}{4} \times 100 = 75%$ . The denominator doesn't matter.

How do I know if 52% makes sense for this problem?

Think logically: $\frac{5.2}{10}$ means 5.2 out of 10 parts. Since 5.2 is slightly more than half of 10, the percentage should be slightly more than 50%. 52% fits perfectly!

What's the difference between 0.52 and 52%?

They represent the same value but in different forms! 0.52 is the decimal form and 52% is the percentage form. Always include the % symbol when expressing as a percentage.

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