If the value of atmospheric pressure is `10^(6)` dyne `cm^(-2)`, find its value in SI units.

Answer

To convert the atmospheric pressure from dyne/cm² to SI units (Newton/m²), we can follow these steps:

### Step 1: Understand the units involved
The given atmospheric pressure is \(10^6\) dyne/cm². We need to convert dyne to Newton and cm² to m².

### Step 2: Convert dyne to Newton
We know that:
\[ 1 \text{ Newton} = 10^5 \text{ dyne} \]
To convert dyne to Newton, we divide by \(10^5\):
\[ \text{Pressure in Newton} = \frac{10^6 \text{ dyne}}{10^5} = 10^{6-5} = 10^1 \text{ Newton} \]

### Step 3: Convert cm² to m²
We also know that:
\[ 1 \text{ meter} = 100 \text{ centimeters} \]
Thus,
\[ 1 \text{ m}^2 = (100 \text{ cm})^2 = 10^4 \text{ cm}^2 \]
To convert cm² to m², we divide by \(10^4\):
\[ \text{Area in m}^2 = \frac{1 \text{ cm}^2}{10^4} = 10^{-4} \text{ m}^2 \]

### Step 4: Combine the conversions
Now we can express the pressure in SI units (Newton/m²):
\[ \text{Pressure in SI units} = \frac{10^1 \text{ Newton}}{10^{-4} \text{ m}^2} = 10^1 \times 10^4 \text{ Newton/m}^2 = 10^{1+4} \text{ Newton/m}^2 = 10^5 \text{ Newton/m}^2 \]

### Final Answer
The value of atmospheric pressure in SI units is:
\[ 10^5 \text{ Newton/m}^2 \]

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