If ` 0 . 13 div p^(2) = 13`, then p is equal to

Options

A. 10
B. `0.01`
C. `0.1`
D. 100

Answer

To solve the equation \( 0.13 \div p^2 = 13 \), we can follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ \frac{0.13}{p^2} = 13 \]

### Step 2: Cross-multiply
To eliminate the fraction, we can cross-multiply:
\[ 0.13 = 13 \cdot p^2 \]

### Step 3: Isolate \( p^2 \)
Now, we can isolate \( p^2 \) by dividing both sides by 13:
\[ p^2 = \frac{0.13}{13} \]

### Step 4: Simplify the fraction
Next, we simplify \( \frac{0.13}{13} \). To do this, we can remove the decimal by multiplying the numerator and the denominator by 100:
\[ p^2 = \frac{0.13 \times 100}{13 \times 100} = \frac{13}{1300} \]

### Step 5: Simplify further
Now we simplify \( \frac{13}{1300} \):
\[ p^2 = \frac{1}{100} \]

### Step 6: Take the square root
To find \( p \), we take the square root of both sides:
\[ p = \sqrt{\frac{1}{100}} = \frac{1}{10} \]

### Final Answer
Thus, the value of \( p \) is:
\[ p = 0.1 \]

---