In this lesson, you will not only focus on unit conversions, you will bring in density. Density will give you an area of focus to apply the many skills you have worked on in this module up to this point. The problems you will work on will not just be plug in the mass and volume and get the density. You will utilize significant digits, prefixes, conversions (this lesson), understanding of SI/Imperial units, and presenting units in the correct style.

Course Competencies and Learning Objectives

A ★ indicates that this page contains content related to that LO.

CC1.1 Solve problems related to scientific units of measurement and significant figures

LO1.1.1 Identify the terms used in scientific communication

LO1.1.2 Apply the rules of significant figures

LO1.1.3 Identify SI and imperial units

LO1.1.4 Match the SI prefixes with their corresponding values

★ LO1.1.5 Apply unit conversion

★ LO1.1.6 Demonstrate units displayed in the correct style

Readings

Physical Science, 13th edition by Bill Tillery McGraw Hill Education

Please read Chapter 1 (section 1.6) in in your textbook.

Media

Converting Units

This lecture video covers unit conversions and the proper way to display units.

Time: 26:58

ASL version of Units & Dimensions

Direct link to non-ASL version

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Lesson: Factor Label Method (Unit Conversion)

This lesson was developed for a non-profit and is Creative Commons licensed by one of our own instructional designers. It is filled with images, audio, and interactive activities. Give it a try.

Link to the interactive lesson

Link to the Study Notes

Water Density (Ice vs Liquid and Buoyancy)

Time: 0:23

Density Lesson with Interactive Practice

This lesson was developed for a non-profit and is Creative Commons licensed by one of our own instructional designers. It is filled with images, audio, and interactive activities. Give it a try.

Link to Interactive lesson

Link to the Study Notes

Practice and Apply

Here are some useful tools for your Practice and Apply work. You might be excellent and not find the following little trick useful, but if algebra is not your strong suite, you will probably love this handy tool. The physics equation for density is

equation:

$ρ = \frac{m}{v}$

In chemistry, density is usually given the letter d in the equation. In physics, the Greek letter $ρ$ represents density.

If you sketched out a triangle with rho (or d for density like it is used in chemistry) on the bottom left, mass at the top, and v in the lower right. Now, whatever variable you are solving for, cover it with your finger. If the variables are side by side, multiply them. If one is over the other, do the division.

Volume = Mass/Density

A finger covers the letter v which is in the lower right representing the denomnator

Solving for volume. image credit: Tammy Moore CC-BY-NC

Mass = Density x Volume

A finger covers the letter m which is in the top representing the numerator

Solving for mass. image credit: Tammy Moore CC-BY-NC

Table of Densities

Use this table of densities to answer some of the Practice and Apply questions.
SUBSTANCE	DENSITY (g/cm³)
Aluminum	2.70
Copper	8.06
Iron	7.87
Lead	11.4
Water	1.00
Seawater	1.03
Mercury	13.6
Gasoline	0.680

PROMPT A block of aluminum has a mass of 0.0081 kg. What is the volume in cm³? Be watchful for potential need to do a unit conversion. Report your answer to the correct number of significant digits and include the correct unit. Note that you will need to use density to solve this one.

Answer

Answer (specifically includes the decimal and zero as well as the units or it is wrong): 3.0 cm³

Not what you got? Study this walkthrough to see where you went wrong.

Given:

mass: 0.0081 kg

aluminum density (from the chart above): 2.70 g/cm³

Find:

volume in cm³

Conversion:

You are given mass in kg but the chart provides densities in g/cm³. You will need to convert.

this pattern tends to be the easiest to remember. Place your given over 1. Then use a conversion factor that will let the given unit be cancelled by it being in the denominator. There are 1000 g in a kg.

$\frac{0.0081 kg}{1} = \frac{1000 g}{1 kg}$

8.1 g, but let's check our significant digits. The value 0.081 has two significant digits because those leading zeros are just placeholders. We will need to then have two significant digits in the answer for this sub-step:

Sub-step: New converted value for mass: 8.1 g

Solve:

shuffle variables -

The equation for density is:

$ρ = \frac{m}{v}$

We could place the numbers in for the variables and then solve for volume, but here to make it clearer to track we will do the algebra before placing the numerical values. We will need to solve for volume. We will move away any variable on the same side as our target variable by doing the opposite operation.

$(\frac{1}{m}) ρ = \frac{m}{v} (\frac{1}{m})$

Let's clean things up a little:

$\frac{ρ}{m} = \frac{1}{v}$

Remember that we are solving for volume. Right now it is in the denominator, so we need to invert the fractions on both sides to get it into the numerator. While we are at it. let's place the v on the left to make it look like a more traditional equation:

$v = \frac{m}{ρ}$

Now, plug in the given values (remember to use the converted mass (g) and not the given mass (kg) -

$v = \frac{8.1}{2.70}$

Right off of your calculator, you get 3. However, you need to report your answer to the correct significant digits. With division, you will examine the numerator and denominator and note the fewest number of digits past the decimal point. The number 8.1 has only one place past the decimal, so you answer should be to one place past the decimal as well to carry the information about the precision of the numbers you were given (assume lab measurement). So, the final answer is ...

3.0 cm³

Supplemental Resources

Equation Sheet - Module 1.pdf