To convert the measurement [tex]\( 8.60 \times 10^8 \frac{ g \cdot cm^2}{s^2} \)[/tex] to [tex]\( \frac{ kg \cdot m^2}{s^2} \)[/tex], follow these steps:
### Step 1: Convert grams (g) to kilograms (kg)
We know that:
[tex]\[ 1 \text{ gram (g)} = 0.001 \text{ kilograms (kg)} \][/tex]
So, if we start with [tex]\( 8.60 \times 10^8 \text{ g} \)[/tex], we need to convert it to kilograms:
[tex]\[ 8.60 \times 10^8 \text{ g} \times 0.001 \frac{ \text{kg} }{ \text{g} } = 8.60 \times 10^8 \times 0.001 \text{ kg} \][/tex]
[tex]\[ = 8.60 \times 10^5 \text{ kg} \][/tex]
[tex]\[ = 860,000 \text{ kg} \][/tex]
### Step 2: Convert square centimeters (cm²) to square meters (m²)
We know that:
[tex]\[ 1 \text{ cm} = 0.01 \text{ m} \][/tex]
So,
[tex]\[ 1 \text{ cm}^2 = (0.01 \text{ m})^2 \][/tex]
[tex]\[ = 0.0001 \text{ m}^2 \][/tex]
Now, convert the [tex]\( \text{cm}^2 \)[/tex] part of the initial measurement:
[tex]\[ 8.60 \times 10^8 \text{ cm}^2 \rightarrow 860,000 \text{ kg} \times 0.0001 \text{ m}^2 \][/tex]
### Step 3: Multiply the converted units together
Now that the mass has been converted to kilograms and the area to square meters:
[tex]\[ 860,000 \text{ kg} \times 0.0001 \frac{ \text{m}^2 }{ \text{cm}^2 } = 860,000 \times 0.0001 \text{ kg} \cdot \text{m}^2 \][/tex]
[tex]\[ = 86 \text{ kg} \cdot \text{m}^2 \][/tex]
### Conclusion
The given measurement [tex]\( 8.60 \times 10^8 \frac{ g \cdot cm^2}{s^2} \)[/tex] is equivalent to [tex]\( 86 \frac{ kg \cdot m^2}{s^2} \)[/tex].
