Convert Fraction to Percentage: Solving 49/102 Through Approximation

Q: How do I know which numbers to round to?

Look for convenient numbers that are close to your original values! For example, 49 is very close to 50, and 102 is close to 100. These make calculations much easier.

Q: What if my approximation seems too different from the original fraction?

Check if your rounded numbers are reasonable. The difference between $ \frac{49}{102} $ and $ \frac{50}{100} $ is very small, so 50% is a good approximation.

Q: How close should my approximation be to the exact answer?

For approximation problems, being within 2-3% of the exact value is usually acceptable. The exact value of $ \frac{49}{102} $ is about 48%, so 50% is excellent!

Q: What if none of the answer choices match my approximation exactly?

Choose the answer choice closest to your approximation. In multiple choice questions, your approximation should clearly point to one correct answer among the options given.

Percentage Conversion with Approximation Techniques

Approximate what is $\frac{49}{102}$ written as a percentage?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert approximately to percentages

00:03 Convert to the closest fraction that we can convert to percentages

00:20 Break down 100 into factors 50 and 2

00:24 Simplify what we can

00:28 This is the simple fraction, now let's convert to percentages

00:32 Multiply the entire fraction by 100, and calculate the quotient

00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Approximate what is $\frac{49}{102}$ written as a percentage?

Step-by-step solution

To approximate the fraction $\frac{49}{102}$ as a percentage, follow these steps:

Recognize that $49$ is close to $50$ and $102$ is slightly more than $100$ . This makes the fraction approximately equal to $\frac{50}{100}$ .
$\frac{50}{100}$ simplifies to $0.5$ .
To find the percentage, multiply $0.5$ by 100: $0.5 \times 100 = 50\%$ .

Therefore, the fraction $\frac{49}{102}$ is approximately $50\%$ when expressed as a percentage.

Final Answer

50%

Key Points to Remember

Essential concepts to master this topic

Approximation Rule: Round numerator and denominator to nearby convenient numbers
Technique: Convert $\frac{49}{102}$ to $\frac{50}{100} = 0.5$
Check: Multiply decimal by 100: 0.5 × 100 = 50% ✓

Common Mistakes

Avoid these frequent errors

Converting exact fraction instead of approximating
Don't calculate $\frac{49}{102} = 0.4804...$ = 48.04%! This gives an unnecessarily precise answer when approximation is asked for. Always round to convenient numbers like $\frac{50}{100}$ first for quick estimation.

Practice Quiz

Test your knowledge with interactive questions

Approximately what is $\frac{11}{50}$ written as a percentage?

FAQ

Everything you need to know about this question

How do I know which numbers to round to?

Look for convenient numbers that are close to your original values! For example, 49 is very close to 50, and 102 is close to 100. These make calculations much easier.

What if my approximation seems too different from the original fraction?

Check if your rounded numbers are reasonable. The difference between $\frac{49}{102}$ and $\frac{50}{100}$ is very small, so 50% is a good approximation.

Do I always need to convert to a fraction with 100 in the denominator?

Not always! You can use any convenient fraction, then convert to percentage. For example, $\frac{1}{2} = 0.5 = 50\%$ works perfectly here.

How close should my approximation be to the exact answer?

For approximation problems, being within 2-3% of the exact value is usually acceptable. The exact value of $\frac{49}{102}$ is about 48%, so 50% is excellent!

What if none of the answer choices match my approximation exactly?

Choose the answer choice closest to your approximation. In multiple choice questions, your approximation should clearly point to one correct answer among the options given.

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