Converting 43/200 to Percentage: Fraction Approximation Problem

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

Percent means "per hundred", so multiplying by 100 converts your fraction into "parts per 100." For example, $ \frac{43}{200} \times 100 = 21.5 $ means 21.5 parts per 100!

Q: How do I know which answer choice to pick when approximating?

Calculate the exact value first (21.5%), then find the closest option. Since 21.5% is closer to 20% than to 25%, choose 20%.

Q: Can I simplify the fraction before converting?

Yes! You can simplify $ \frac{43}{200} $ first, but since 43 and 200 share no common factors, it's already in simplest form. Just multiply by 100 directly.

Q: What if I get a different decimal when I calculate?

Double-check your division: $ 4300 ÷ 200 = 21.5 $. Make sure you're dividing 4300 (not 43) by 200 to get the correct percentage.

Q: Is 21.5% really approximately 20%?

Yes! In approximation problems, look for the nearest reasonable value. 21.5% is only 1.5% away from 20%, making it the best choice among the given options.

Fraction to Percentage with Approximation

Approximately what is $\frac{43}{200}$ 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 Let's convert to the closest fraction we can change to percentages

00:16 Let's break down 200 into factors 40 and 5

00:23 Let's convert to the closest fraction we can change to percentages:

00:26 This is the simple fraction, now let's convert to percentages

00:33 Let's 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

Approximately what is $\frac{43}{200}$ written as a percentage?

Step-by-step solution

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

Step 1: Convert the fraction $\frac{43}{200}$ to a percentage by multiplying it by 100.
Step 2: Calculate the value to obtain the percentage.
Step 3: Match the calculated percentage with the given multiple-choice options.

Now, let's work through each step:
Step 1: We start by multiplying the fraction by 100. This gives us:

\left(\frac{43}{200} \times 100\right) \%

Step 2: Simplify the expression. First, calculate $\frac{43 \times 100}{200}$ .

\frac{4300}{200} = 21.5

Step 3: Since the question focuses on estimation, we recognize that 21.5% is approximately equal to 20%.

Therefore, the approximate percentage representation of the fraction $\frac{43}{200}$ is 20%.

Final Answer

20%

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to percentages by multiplying by 100
Technique: Calculate $\frac{43 \times 100}{200} = \frac{4300}{200} = 21.5\%$
Check: Round 21.5% to nearest given option: 20% ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100 when converting to percentage
Don't just convert $\frac{43}{200}$ to 0.215 and call it done = missing the % symbol! This gives a decimal, not a percentage. Always multiply by 100 to convert from decimal to percentage form.

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

Why do I multiply by 100 to get a percentage?

Percent means "per hundred", so multiplying by 100 converts your fraction into "parts per 100." For example, $\frac{43}{200} \times 100 = 21.5$ means 21.5 parts per 100!

How do I know which answer choice to pick when approximating?

Calculate the exact value first (21.5%), then find the closest option. Since 21.5% is closer to 20% than to 25%, choose 20%.

Can I simplify the fraction before converting?

Yes! You can simplify $\frac{43}{200}$ first, but since 43 and 200 share no common factors, it's already in simplest form. Just multiply by 100 directly.

What if I get a different decimal when I calculate?

Double-check your division: $4300 ÷ 200 = 21.5$ . Make sure you're dividing 4300 (not 43) by 200 to get the correct percentage.

Is 21.5% really approximately 20%?

Yes! In approximation problems, look for the nearest reasonable value. 21.5% is only 1.5% away from 20%, making it the best choice among the given options.

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