The value of `(20 xx (0.3)^(2))/(0.018) div 0.5 ` of `0.2` is

Options

A. 10
B. 100
C. 20
D. 1000

Answer

To solve the expression \((20 \times (0.3)^{2})/(0.018) \div 0.5 \text{ of } 0.2\), we will follow these steps:

### Step 1: Rewrite the expression in fractional form
We start by converting the decimal numbers into fractions:
- \(0.3 = \frac{3}{10}\)
- \(0.018 = \frac{18}{1000}\)
- \(0.5 = \frac{5}{10}\)
- \(0.2 = \frac{2}{10}\)

Now, we can rewrite the expression:
\[ \frac{20 \times \left(\frac{3}{10}\right)^{2}}{\frac{18}{1000}} \div \left(\frac{5}{10} \times \frac{2}{10}\right) \]

### Step 2: Simplify the expression
First, calculate \((\frac{3}{10})^{2}\):
\[ \left(\frac{3}{10}\right)^{2} = \frac{9}{100} \]
Now substitute this back into the expression:
\[ \frac{20 \times \frac{9}{100}}{\frac{18}{1000}} \div \left(\frac{5 \times 2}{10 \times 10}\right) \]

Next, calculate \(5 \times 2\) and \(10 \times 10\):
\[ 5 \times 2 = 10 \quad \text{and} \quad 10 \times 10 = 100 \]
Thus, we have:
\[ \frac{20 \times \frac{9}{100}}{\frac{18}{1000}} \div \frac{10}{100} \]

### Step 3: Handle the division
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we rewrite the expression:
\[ \frac{20 \times \frac{9}{100}}{\frac{18}{1000}} \times \frac{100}{10} \]

### Step 4: Simplify the fractions
Now we can simplify:
1. Multiply the numerators:
\[ 20 \times 9 = 180 \]
2. The denominator of the first fraction becomes:
\[ \frac{18}{1000} \Rightarrow 180 \div \frac{18}{1000} = 180 \times \frac{1000}{18} \]

### Step 5: Cancel out common factors
Now simplify \(180 \times \frac{1000}{18}\):
\[ 180 \div 18 = 10 \quad \text{thus,} \quad 10 \times 1000 = 10000 \]

### Step 6: Final multiplication
Now multiply by \(\frac{100}{10}\):
\[ 10000 \times \frac{100}{10} = 10000 \times 10 = 100000 \]

### Final Answer
Thus, the value of the expression is:
\[ \text{Final Answer} = 1000 \]