The least number among `(4)/(9) , sqrt((9)/(49)) , 0.45 and (0.8)^(2)` is

Options

A. a) `(4)/(9)`
B. b) `sqrt((9)/(49))`
C. c) `0.45`
D. d) `(0.8)^(2)`

Answer

To find the least number among the given values \( \frac{4}{9} \), \( \sqrt{\frac{9}{49}} \), \( 0.45 \), and \( (0.8)^2 \), we will convert each value to decimal form for easier comparison.

### Step 1: Convert \( \frac{4}{9} \) to decimal
To convert \( \frac{4}{9} \) to decimal, we divide 4 by 9.

\[ \frac{4}{9} \approx 0.4444 \ldots \text{ (repeating)} \]

### Step 2: Calculate \( \sqrt{\frac{9}{49}} \)
Next, we simplify \( \sqrt{\frac{9}{49}} \):

\[ \sqrt{\frac{9}{49}} = \frac{\sqrt{9}}{\sqrt{49}} = \frac{3}{7} \]

Now, we convert \( \frac{3}{7} \) to decimal:

\[ \frac{3}{7} \approx 0.4286 \ldots \]

### Step 3: Compare \( 0.45 \) with the previous results
The decimal value of \( 0.45 \) is already in decimal form.

### Step 4: Calculate \( (0.8)^2 \)
Now, we calculate \( (0.8)^2 \):

\[ (0.8)^2 = 0.64 \]

### Step 5: Compare all values
Now we have the following decimal values:
- \( \frac{4}{9} \approx 0.4444 \)
- \( \sqrt{\frac{9}{49}} \approx 0.4286 \)
- \( 0.45 \)
- \( (0.8)^2 = 0.64 \)

### Step 6: Identify the least number
Comparing all these values:
- \( 0.4286 \) (from \( \sqrt{\frac{9}{49}} \))
- \( 0.4444 \) (from \( \frac{4}{9} \))
- \( 0.45 \)
- \( 0.64 \)

The least number among these is \( 0.4286 \), which corresponds to \( \sqrt{\frac{9}{49}} \).

### Conclusion
Thus, the least number among \( \frac{4}{9} \), \( \sqrt{\frac{9}{49}} \), \( 0.45 \), and \( (0.8)^2 \) is:

\[ \sqrt{\frac{9}{49}} \]