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

Options

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

Answer

To find the least number among the given values \( \frac{4}{9}, \sqrt{\frac{9}{49}}, 0.45, \text{ and } (0.8)^2 \), we will convert each of these values into decimal form and then compare them.

### Step 1: Convert \( \frac{4}{9} \) to decimal
To convert \( \frac{4}{9} \) to decimal, we can perform the division:
\[ \frac{4}{9} \approx 0.4444\ldots \text{ (which is } 0.4\overline{4} \text{)} \]

**Hint:** Divide the numerator by the denominator to convert a fraction to a decimal.

### Step 2: Convert \( \sqrt{\frac{9}{49}} \) to decimal
First, simplify \( \sqrt{\frac{9}{49}} \):
\[ \sqrt{\frac{9}{49}} = \frac{\sqrt{9}}{\sqrt{49}} = \frac{3}{7} \]
Now, convert \( \frac{3}{7} \) to decimal:
\[ \frac{3}{7} \approx 0.4285714\ldots \text{ (which is approximately } 0.4285 \text{)} \]

**Hint:** Use the property of square roots and simplify before converting to decimal.

### Step 3: Identify the decimal value of \( 0.45 \)
The value \( 0.45 \) is already in decimal form, so we can keep it as is.

**Hint:** No conversion is needed for numbers already in decimal form.

### Step 4: Convert \( (0.8)^2 \) to decimal
Calculate \( (0.8)^2 \):
\[ (0.8)^2 = 0.64 \]

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

### Step 5: Compare all decimal values
Now we have the following decimal values:
- \( \frac{4}{9} \approx 0.4444\ldots \)
- \( \sqrt{\frac{9}{49}} \approx 0.4285 \)
- \( 0.45 \)
- \( (0.8)^2 = 0.64 \)

Now, we can compare these values:
- \( 0.4444\ldots \)
- \( 0.4285 \)
- \( 0.45 \)
- \( 0.64 \)

The least number among these is \( 0.4285 \) (which corresponds to \( \sqrt{\frac{9}{49}} \)).

### Final Answer
Therefore, the least number among \( \frac{4}{9}, \sqrt{\frac{9}{49}}, 0.45, \text{ and } (0.8)^2 \) is:
\[ \sqrt{\frac{9}{49}} \]

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