A flask containing \(11.7 \mathrm{~mL}\) of a liquid weighs \(132.8 \mathrm{~g}\) with the liquid in the flask and \(124.1 \mathrm{~g}\) when empty. Calculate the density of the liquid in \(\mathrm{g} / \mathrm{mL}\) to the correct number of significant digits. MISSED THIS? Read Section 1.6; Watch KCV 1.7, IWE 1.6

Understanding significant digits is crucial when reporting the results of your calculations in science and engineering. These digits include all the non-zero numbers, any zeros between them, and any trailing zeros in a decimal quantity. Why are they important? Well, they give us an insight into the precision of the measurements involved in our calculations.

Let's apply this concept to our problem at hand. In the exercise, we have two measurements: the mass of the flask with liquid (132.8 g) and the volume of the liquid (11.7 mL). Both measurements have three significant digits. When performing calculations, like finding the density, we need to report our final answer with the same level of precision. That means, even if our calculation gives us a long decimal, we'd round it to three significant digits. It ensures that our answer doesn't falsely imply a higher degree of precision than the original data provided.

Mass and volume are fundamental concepts in physics. Mass refers to the amount of matter in an object and is often measured in grams (g) or kilograms (kg). Volume, on the other hand, is the space that an object occupies, measured in liters (L), milliliters (mL), or cubic centimeters (cm³).

In the context of our problem, mass and volume are used to determine the density of a liquid. As seen in the step-by-step solution, we calculate the mass of the liquid by finding the difference between the mass of the flask with liquid and the empty flask. This strategy removes the weight of the flask itself, leaving us with the pure mass of the liquid. Understanding the relationship between mass and volume is key to many scientific disciplines, as they're used to calculate properties such as density, concentration, and buoyancy.

The density of a substance is a measure of its mass per unit volume. This is a crucial property in various scientific fields, particularly chemistry and physics. The formula for density is quite straightforward:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
In our problem, once you've found the mass of the liquid (by subtracting the mass of the empty flask from the full flask’s mass), you simply divide that mass by the liquid’s volume. This will give you the liquid's density. For example, if a liquid has a mass of 50 g and occupies a volume of 10 mL, its density would be:
\[ \text{Density} = \frac{50 \, \text{g}}{10 \, \text{mL}} = 5 \, \text{g/mL} \]
When you perform your calculation, make sure the final answer has the correct number of significant digits as determined from the given values in the problem. Using the density formula correctly while taking into account units and significant digits allows for precise and meaningful scientific communication.