Calculate Percentage: Converting 256 to a Percentage of 16

Q: Can a percentage be more than 100%?

Absolutely! When the part is larger than the whole, you get percentages over 100%. In this case, 256 is 16 times bigger than 16, so it's 1600%.

Q: Why is the answer 1600% and not 16%?

Don't forget the final step! After dividing $ \frac{256}{16} = 16 $, you must multiply by 100% to convert to percentage form: 16 × 100% = 1600%.

Q: How do I remember the percentage formula?

Think of it as 'What I want to find' ÷ 'What I'm comparing to' × 100%. Here, we want to find what percentage 256 is, compared to 16.

Q: What does 1600% actually mean?

It means 256 is 16 times as large as 16. Since 100% means 'the same size', 1600% means '16 times the original size'.

Percentage Calculations with Values Greater Than Base

What is the percentage of 256 over 16?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find out what percentage 256 is of 16.

00:09 We'll use the usual formula for calculating percentages.

00:14 First, divide 256 by 16, then multiply the result by 100.

00:21 Think of 256 as 16 times 16. This makes it easier.

00:27 Simplify wherever you can, to make it neat.

00:34 And there you have it! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the percentage of 256 over 16?

Step-by-step solution

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

Step 1: Identify the given information -- to find what percentage 256 is of 16.
Step 2: Apply the formula for percentage conversion.
Step 3: Calculate the result by performing the necessary arithmetic operations.

Let's proceed with the calculation:

Step 1: We are given that the part (numerator) is 256 and the whole (denominator) is 16.

Step 2: Use the formula for percentage:

\text{percentage} = \left( \frac{256}{16} \right) \times 100\%

Step 3: Calculate the division:

\frac{256}{16} = 16

Then, convert this to a percentage:

16 \times 100\% = 1600\%

Therefore, the percentage of 256 over 16 is $1600\%$ .

According to the given choices, the correct answer is choice 4: 1600%.

Final Answer

1600%

Key Points to Remember

Essential concepts to master this topic

Formula: Percentage = (part ÷ whole) × 100%
Technique: Calculate 256 ÷ 16 = 16, then 16 × 100% = 1600%
Check: If 16 × 1600% = 16 × 16 = 256 ✓

Common Mistakes

Avoid these frequent errors

Confusing which number is the part and which is the whole
Don't calculate 16 ÷ 256 × 100% = 6.25%! This reverses the question and asks what percentage 16 is of 256. Always read carefully: '256 over 16' means 256 ÷ 16.

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

Can a percentage be more than 100%?

Absolutely! When the part is larger than the whole, you get percentages over 100%. In this case, 256 is 16 times bigger than 16, so it's 1600%.

Why is the answer 1600% and not 16%?

Don't forget the final step! After dividing $\frac{256}{16} = 16$ , you must multiply by 100% to convert to percentage form: 16 × 100% = 1600%.

How do I remember the percentage formula?

Think of it as 'What I want to find' ÷ 'What I'm comparing to' × 100%. Here, we want to find what percentage 256 is, compared to 16.

What does 1600% actually mean?

It means 256 is 16 times as large as 16. Since 100% means 'the same size', 1600% means '16 times the original size'.

Is there a shortcut for this type of problem?

Yes! If you can easily divide the numbers, do that first. Since $256 ÷ 16 = 16$ , just add two zeros: 16 becomes 1600%.

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