Questions: 40 * dL^2 / 0.50 L = ?

Transcript text: $\frac{40 \cdot \mathrm{dL}^{2}}{0.50 \mathrm{~L}}=?$

Solution

Solution Steps

To solve the given expression, we need to simplify the fraction by performing the division. The expression involves multiplying 40 by $ \mathrm{dL}^2 $ and then dividing by 0.50 L. We will perform the arithmetic operation and simplify the units accordingly.

Step 1: Simplify the Expression

The given expression is $\frac{40 \cdot \mathrm{dL}^{2}}{0.50 \, \mathrm{L}}$. To simplify, we perform the division of the numerical coefficients:

\[ \frac{40}{0.50} = 80 \]

Step 2: Simplify the Units

The units in the expression are $\mathrm{dL}^2$ in the numerator and $\mathrm{L}$ in the denominator. We know that $1 \, \mathrm{dL} = 0.1 \, \mathrm{L}$, so:

\[ \mathrm{dL}^2 = (0.1 \, \mathrm{L})^2 = 0.01 \, \mathrm{L}^2 \]

Thus, the units simplify as follows:

\[ \frac{\mathrm{dL}^2}{\mathrm{L}} = \frac{0.01 \, \mathrm{L}^2}{\mathrm{L}} = 0.01 \, \mathrm{L} \]

Step 3: Combine the Results

Combine the numerical result with the simplified units:

\[ 80 \times 0.01 \, \mathrm{L} = 0.8 \, \mathrm{L} \]