`{((0.1)^(2) - (0.01)^(2))/(0.0001) + 1}` is equal to

Options

A. 1010
B. 110
C. 101
D. 100

Answer

To solve the expression \(\frac{(0.1)^{2} - (0.01)^{2}}{0.0001} + 1\), we can follow these steps:

### Step 1: Calculate \((0.1)^{2}\) and \((0.01)^{2}\)
\[ (0.1)^{2} = 0.01 \]
\[ (0.01)^{2} = 0.0001 \]

### Step 2: Substitute the values into the expression
Now substitute these values into the expression:
\[ \frac{0.01 - 0.0001}{0.0001} + 1 \]

### Step 3: Perform the subtraction in the numerator
Calculate \(0.01 - 0.0001\):
\[ 0.01 - 0.0001 = 0.0099 \]

### Step 4: Substitute back into the expression
Now substitute this result back into the expression:
\[ \frac{0.0099}{0.0001} + 1 \]

### Step 5: Perform the division
Calculate \(\frac{0.0099}{0.0001}\):
\[ \frac{0.0099}{0.0001} = 99 \]

### Step 6: Add 1 to the result
Now add 1 to the result:
\[ 99 + 1 = 100 \]

### Final Result
Thus, the final result of the expression is:
\[ \boxed{100} \]