`{((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: Identify the expression
We start with the expression:
\[ \frac{(0.1)^2 - (0.01)^2}{0.0001} + 1 \]

### Step 2: Calculate the squares
Calculate \((0.1)^2\) and \((0.01)^2\):
\[ (0.1)^2 = 0.01 \]
\[ (0.01)^2 = 0.0001 \]

### Step 3: Substitute the squares back into the expression
Substituting these values back into the expression gives:
\[ \frac{0.01 - 0.0001}{0.0001} + 1 \]

### Step 4: Simplify the numerator
Now, simplify the numerator:
\[ 0.01 - 0.0001 = 0.0099 \]
So we have:
\[ \frac{0.0099}{0.0001} + 1 \]

### Step 5: Divide the numerator by the denominator
Next, we divide \(0.0099\) by \(0.0001\):
\[ \frac{0.0099}{0.0001} = 99 \]
Thus, the expression simplifies to:
\[ 99 + 1 \]

### Step 6: Add 1 to the result
Finally, we add \(1\) to \(99\):
\[ 99 + 1 = 100 \]

### Final Answer
Therefore, the expression \(\frac{(0.1)^2 - (0.01)^2}{0.0001} + 1\) is equal to \(100\).

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