Converting 7.8/10: Fraction to Percentage Solution

Q: Why can't I just put a % sign after 7.8/10?

Percentages mean 'out of 100', not 'out of 10'. You need to convert the fraction so the denominator becomes 100, which gives you $ \frac{78}{100} = 78\% $.

Q: What's the difference between 0.78 and 78%?

They represent the same value but in different forms! 0.78 is the decimal form while 78% is the percentage form. Think of it like saying 'three-quarters' vs 'seventy-five percent'.

Q: Can I convert 7.8/10 to 78/100 directly?

Yes! Multiply both numerator and denominator by 10: $ \frac{7.8 \times 10}{10 \times 10} = \frac{78}{100} = 78\% $. This is actually the same process as the decimal method!

Q: What if the denominator isn't 10 or 100?

No problem! Always divide first to get the decimal, then multiply by 100. For example: $ \frac{3}{8} = 0.375 $, then 0.375 × 100 = 37.5%.

Q: Why do we multiply by 100 to get percentage?

Because 'percent' literally means 'per hundred'! When you multiply by 100, you're converting from 'per 1' (decimal) to 'per 100' (percentage). It's like converting units!

Fraction to Percentage with Decimal Numerators

Convert the fraction $\frac{7.8}{10}$ to a percentage:

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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 To convert a fraction to a percentage, the denominator needs to be 100

00:10 The percentage is the numerator (X)

00:15 Apply this formula to our exercise

00:20 Multiply both the numerator and denominator by 10 to obtain a denominator equal to 100

00:25 Proceed to calculate

00:39 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert the fraction $\frac{7.8}{10}$ to a percentage:

Step-by-step solution

To convert the fraction $\frac{7.8}{10}$ into a percentage, we follow these simple steps:

Step 1: Understand that converting a fraction to a percentage involves multiplying by 100.
Step 2: Express the fraction given as a decimal by performing the division $\frac{7.8}{10} = 0.78$ .
Step 3: Multiply the decimal by 100 to convert it to a percentage: $0.78 \times 100 = 78$ . This gives us $78\%$ .

Therefore, converting the fraction $\frac{7.8}{10}$ to a percentage, we get $78\%$ .

Final Answer

78%

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fraction to decimal first, then multiply by 100
Technique: $\frac{7.8}{10} = 0.78$ , then 0.78 × 100 = 78%
Check: 78% equals 0.78 as decimal, and 0.78 × 10 = 7.8 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100 after finding the decimal
Don't stop at 0.78 = finished! This gives you the decimal form, not percentage. Always multiply the decimal by 100 to convert to percentage form.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction $\frac{75}{100}$

to a percentage:

FAQ

Everything you need to know about this question

Why can't I just put a % sign after 7.8/10?

Percentages mean 'out of 100', not 'out of 10'. You need to convert the fraction so the denominator becomes 100, which gives you $\frac{78}{100} = 78\%$ .

What's the difference between 0.78 and 78%?

They represent the same value but in different forms! 0.78 is the decimal form while 78% is the percentage form. Think of it like saying 'three-quarters' vs 'seventy-five percent'.

Can I convert 7.8/10 to 78/100 directly?

Yes! Multiply both numerator and denominator by 10: $\frac{7.8 \times 10}{10 \times 10} = \frac{78}{100} = 78\%$ . This is actually the same process as the decimal method!

What if the denominator isn't 10 or 100?

No problem! Always divide first to get the decimal, then multiply by 100. For example: $\frac{3}{8} = 0.375$ , then 0.375 × 100 = 37.5%.

Why do we multiply by 100 to get percentage?

Because 'percent' literally means 'per hundred'! When you multiply by 100, you're converting from 'per 1' (decimal) to 'per 100' (percentage). It's like converting units!

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