`(1)/(33) `of `(1)/(66) `of` (1)/(3)` of `(1)/(66) `of ` 10000` of a number will be what percentage of that number ?

Options

A. `2.32`
B. `1.32`
C. `0.232`
D. `0.0232`

Answer

To solve the problem step by step, we will follow the mathematical operations as outlined in the video transcript.

### Step-by-Step Solution:

1. **Assume the number**: Let the number be \( x \).

2. **Set up the expression**: We need to calculate:
\[ \frac{1}{33} \text{ of } \frac{1}{66} \text{ of } \frac{1}{3} \text{ of } \frac{1}{66} \text{ of } 10000 \text{ of } x \]
This can be expressed as:
\[ \frac{1}{33} \times \frac{1}{66} \times \frac{1}{3} \times \frac{1}{66} \times 10000 \times x \]

3. **Combine the fractions**: First, we will multiply the fractions:
\[ \frac{1}{33} \times \frac{1}{66} \times \frac{1}{3} \times \frac{1}{66} = \frac{1}{33 \times 66 \times 3 \times 66} \]

4. **Calculate the denominator**:
- First, calculate \( 33 \times 66 \):
\[ 33 \times 66 = 2178 \]
- Now, calculate \( 2178 \times 3 \):
\[ 2178 \times 3 = 6534 \]
- Finally, calculate \( 6534 \times 66 \):
\[ 6534 \times 66 = 430224 \]
Therefore, we have:
\[ \frac{1}{430224} \]

5. **Combine with 10000**:
Now, we multiply by \( 10000 \):
\[ \frac{10000}{430224} \times x \]

6. **Simplify the fraction**:
To simplify \( \frac{10000}{430224} \), we can divide both the numerator and the denominator by 10000:
\[ \frac{10000 \div 10000}{430224 \div 10000} = \frac{1}{43.0224} \]

7. **Calculate the percentage**:
We need to find what percentage this value is of \( x \):
\[ \frac{1}{43.0224} \times x = 0.0232x \]
To express this as a percentage:
\[ 0.0232 \times 100 = 2.32\% \]

### Final Answer:
Thus, the value is approximately **2.32%** of the number \( x \).