`(0.2 xx 0.2 + 0.01) (0.1 xx 0.1 + 0.02)^(-1)` is equal to

Options

A. A) `(5)/(3)`
B. B) `(41)/(12)`
C. C) `(41)/(4)`
D. D)`(9)/(5)`

Answer

To solve the expression `(0.2 x 0.2 + 0.01) (0.1 x 0.1 + 0.02)^(-1)`, we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the first bracket:**
\[ 0.2 \times 0.2 + 0.01 \]
- First, calculate \(0.2 \times 0.2\):
\[ 0.2 \times 0.2 = 0.04 \]
- Now, add \(0.01\):
\[ 0.04 + 0.01 = 0.05 \]

2. **Calculate the second bracket:**
\[ 0.1 \times 0.1 + 0.02 \]
- First, calculate \(0.1 \times 0.1\):
\[ 0.1 \times 0.1 = 0.01 \]
- Now, add \(0.02\):
\[ 0.01 + 0.02 = 0.03 \]

3. **Find the inverse of the second bracket:**
\[ (0.03)^{-1} \]
- The inverse of \(0.03\) is:
\[ \frac{1}{0.03} = \frac{100}{3} \]

4. **Combine the results:**
Now substitute back into the original expression:
\[ 0.05 \times \frac{100}{3} \]
- Convert \(0.05\) to a fraction:
\[ 0.05 = \frac{5}{100} = \frac{1}{20} \]
- Now multiply:
\[ \frac{1}{20} \times \frac{100}{3} = \frac{100}{60} = \frac{5}{3} \]

### Final Answer:
The expression evaluates to:
\[ \frac{5}{3} \]