The greatest number among the following is
`(4)/(9)`, `sqrt((9)/(49))`, `.47`, `0.7^2`

Options

A. `(4)/(9)`
B. `sqrt((9)/(49))`
C. `.47`
D. `(0.7)^(2)`

Answer

To find the greatest number among the given options, we will evaluate each number step by step.

1. **Evaluate \( \frac{4}{9} \)**:
\[ \frac{4}{9} \approx 0.4444 \quad (\text{repeating}) \]

**Hint**: Divide 4 by 9 to get a decimal approximation.

2. **Evaluate \( \sqrt{\frac{9}{49}} \)**:
\[ \sqrt{\frac{9}{49}} = \frac{\sqrt{9}}{\sqrt{49}} = \frac{3}{7} \approx 0.4286 \]

**Hint**: Use the property of square roots to simplify the fraction before calculating.

3. **Evaluate \( 0.47 \)**:
\[ 0.47 \quad (\text{already in decimal form}) \]

**Hint**: This number is already given in decimal form, so no calculation is needed.

4. **Evaluate \( 0.7^2 \)**:
\[ 0.7^2 = 0.49 \]

**Hint**: Square the number 0.7 to find its value.

Now, we have the following decimal approximations:
- \( \frac{4}{9} \approx 0.4444 \)
- \( \sqrt{\frac{9}{49}} \approx 0.4286 \)
- \( 0.47 \)
- \( 0.7^2 = 0.49 \)

Next, we compare these values:
- \( 0.4444 \)
- \( 0.4286 \)
- \( 0.47 \)
- \( 0.49 \)

The greatest number among these is \( 0.49 \).

**Final Answer**: The greatest number is \( 0.7^2 \) or \( 0.49 \).