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 $3333.33\%$.

Steps to Solve

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:

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

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:

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

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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