Which is the correct ascending order ascending order of the given number ?

Options

A. `(1)/(3),(4)/(15),0.33`
B. `(1)/(3),0.33,(4)/(15)`
C. `(4)/(15),0.33,(1)/(3)`
D. `0.33,(4)/(15),(1)/(3)`

Answer

To determine the correct ascending order of the given numbers \( \frac{1}{3} \), \( \frac{4}{15} \), and \( 0.33 \), we will first convert all the fractions to decimal form for easier comparison.

### Step-by-Step Solution:

1. **Convert \( \frac{1}{3} \) to Decimal:**
\[ \frac{1}{3} = 0.3333\ldots \quad (\text{This is a recurring decimal}) \]

2. **Convert \( \frac{4}{15} \) to Decimal:**
\[ \frac{4}{15} = 0.2666\ldots \quad (\text{This is also a recurring decimal}) \]

3. **Identify the Decimal for \( 0.33 \):**
\[ 0.33 = 0.33 \quad (\text{This is a terminating decimal}) \]

4. **List the Decimals:**
- \( \frac{1}{3} \approx 0.3333\ldots \)
- \( \frac{4}{15} \approx 0.2666\ldots \)
- \( 0.33 = 0.33 \)

5. **Compare the Decimals:**
- \( 0.2666\ldots < 0.33 < 0.3333\ldots \)

6. **Arrange in Ascending Order:**
\[ \frac{4}{15} < 0.33 < \frac{1}{3} \]

Thus, the correct ascending order of the given numbers is:
\[ \frac{4}{15}, 0.33, \frac{1}{3} \]

### Final Answer:
The correct ascending order is \( \frac{4}{15}, 0.33, \frac{1}{3} \).