Question

fill in the blanks with the correct numerical value rounded appropriately and with the correct significant figures.

an object with a mass of 5.18 grams and a density of 1.041 g/ml will have a volume of □ ml.

an object with a volume of 4.88 ml and a density of 0.997 g/ml will have a mass of □ grams.

Explanation:

First Problem (Volume Calculation)

Step1: Recall density formula

The formula for density is $
ho = \frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume. We need to solve for $V$, so rearrange the formula to $V=\frac{m}{
ho}$.

Step2: Substitute values

Given $m = 5.18\space g$ and $
ho=1.041\space g/mL$. Substitute into the formula: $V=\frac{5.18}{1.041}$.

Step3: Calculate and round

Calculate $\frac{5.18}{1.041}\approx4.97598$. Now, consider significant figures. The mass has 3 significant figures, and the density has 4. When dividing, the result should have the same number of significant figures as the least precise measurement (3 in this case). So we round to 3 significant figures: $4.98$.

Second Problem (Mass Calculation)

Step1: Recall density formula

Using $
ho = \frac{m}{V}$, solve for $m$: $m=
ho\times V$.

Step2: Substitute values

Given $V = 4.88\space mL$ and $
ho = 0.997\space g/mL$. Substitute: $m = 0.997\times4.88$.

Step3: Calculate and round

Calculate $0.997\times4.88 = 4.86536$. The volume has 3 significant figures, and the density has 3. When multiplying, the result should have 3 significant figures. So we round to 3 significant figures: $4.87$.

Answer:

First blank: $4.98$
Second blank: $4.87$