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
- 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.