Converting 128% to Its Decimal Form: Percentage Mathematics

Q: Why do I need to simplify the fraction after converting from percentage?

Simplifying gives you the cleanest, most reduced form that's easier to work with in calculations. $ \frac{32}{25} $ is much simpler than $ \frac{128}{100} $!

Q: How do I find the GCD of 128 and 100?

List the factors of each number or use the Euclidean algorithm. For 128 and 100, common factors are 1, 2, and 4. The greatest is 4, so GCD = 4.

Q: Can I convert 128% to a decimal instead?

Yes! $ 128\% = 1.28 $ as a decimal. But when the question asks for a fraction, you must express it as $ \frac{32}{25} $.

Q: What if the percentage doesn't simplify evenly?

Some percentages create fractions that are already in lowest terms. Always check for common factors first - if there aren't any, your fraction is already simplified!

Q: How can I check if my simplified fraction is correct?

Convert back to decimal: $ \frac{32}{25} = 32 ÷ 25 = 1.28 $, then multiply by 100 to get 128%. If it matches the original percentage, you're right!

Percentage to Fraction with Simplification

The percentage 128% is equal to:

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert from percentages to fractions

00:05 The percentage equals a fraction where the numerator is the percentage (X) and the denominator is 100

00:10 Apply this formula to our exercise

00:30 Break down 128 into factors of 32 and 4, and 100 into factors of 25 and 4

00:35 Reduce wherever possible

00:40 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The percentage 128% is equal to:

Step-by-step solution

To convert the percentage 128% to a fraction, we begin by expressing 128% as a fraction over 100:

$128\% = \frac{128}{100}$

Next, we simplify the fraction $\frac{128}{100}$ . We do this by finding the greatest common divisor (GCD) of 128 and 100. The GCD of 128 and 100 is 4.

We divide both the numerator and the denominator by their GCD:

$\frac{128 \div 4}{100 \div 4} = \frac{32}{25}$

Therefore, 128% is equal to the fraction $\frac{32}{25}$ .

Thus, in the context of the provided multiple-choice answers, the correct choice is $\frac{32}{25}$ , which corresponds to choice 3.

The simplified fraction representation of 128% is $\frac{32}{25}$ .

Final Answer

$\frac{32}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentage by placing over 100, then simplify
Technique: Find GCD of 128 and 100 which is 4
Check: Verify $\frac{32}{25} = 1.28 = 128\%$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction after converting
Don't leave $\frac{128}{100}$ as your final answer = incomplete solution! This fraction can be reduced further. Always find the GCD and divide both numerator and denominator to get the simplest form.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{24}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do I need to simplify the fraction after converting from percentage?

Simplifying gives you the cleanest, most reduced form that's easier to work with in calculations. $\frac{32}{25}$ is much simpler than $\frac{128}{100}$ !

How do I find the GCD of 128 and 100?

List the factors of each number or use the Euclidean algorithm. For 128 and 100, common factors are 1, 2, and 4. The greatest is 4, so GCD = 4.

Can I convert 128% to a decimal instead?

Yes! $128\% = 1.28$ as a decimal. But when the question asks for a fraction, you must express it as $\frac{32}{25}$ .

What if the percentage doesn't simplify evenly?

Some percentages create fractions that are already in lowest terms. Always check for common factors first - if there aren't any, your fraction is already simplified!

How can I check if my simplified fraction is correct?

Convert back to decimal: $\frac{32}{25} = 32 ÷ 25 = 1.28$ , then multiply by 100 to get 128%. If it matches the original percentage, you're right!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Percentage questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime