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What is the percentage of 33 1/3?

Understand the Problem

The question is asking for the percentage representation of the fraction 33 1/3. To convert a fraction to a percentage, we multiply it by 100. In this case, we will first convert the mixed number to an improper fraction and then calculate the percentage.

Answer

The percentage representation is approximately $3333.33\%$.
Answer for screen readers

The percentage representation of the fraction (33 \frac{1}{3}) is approximately (3333.33%).

Steps to Solve

  1. Convert the mixed number to an improper fraction

To convert the mixed number (33 \frac{1}{3}) into an improper fraction, we multiply the whole number by the denominator and add the numerator. Thus, we have:

$$ 33 \frac{1}{3} = \frac{33 \times 3 + 1}{3} = \frac{99 + 1}{3} = \frac{100}{3} $$

  1. Multiply by 100 to find the percentage

Now that we have the improper fraction ( \frac{100}{3} ), we can convert it to a percentage by multiplying by 100:

$$ \frac{100}{3} \times 100 = \frac{10000}{3} $$

  1. Calculate the percentage value

Next, we perform the division:

$$ \frac{10000}{3} \approx 3333.33 $$

Thus, the percentage representation of (33 \frac{1}{3}) is approximately (3333.33%).

The percentage representation of the fraction (33 \frac{1}{3}) is approximately (3333.33%).

More Information

This calculation shows how a mixed number can be transformed into a percentage. The conversion involves first turning the mixed number into an improper fraction and then finding its percentage equivalent, which signifies a very large representation in a percentage form.

Tips

  • Mistaking the whole number part and not converting it correctly to an improper fraction.
  • Forgetting to multiply the fraction by 100 to derive the percentage.
  • Rounding too early in calculations, which can lead to inaccuracy in the final result.
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