## Math Skills - Dimensional Analysis

Trigonometry and Solving Physics Problems. Sometimes people need to analyze the horizontal and vertical components of forces and object orientation. When the force or object is not acting parallel to the x or y axis, people can employ basic trigonometry to use . Converting between metric units is called unit analysis or dimensional analysis. Unit analysis is a form of proportional reasoning where a given measurement can be multiplied by a known proportion or ratio to give a result having a different unit or dimension. Algebraically, we know that any number multiplied by one will be unchanged. Solve one-step and multi-step problems using dimensional analysis and conversion factors Explain how to cancel out numerator and denominator units To unlock this lesson you must be a .

## Fun with Dimensional Analysis

Density is a physical property and demonstrates the relationship between mass and volume of a material. If you take one mL of water and put it on a balance, you'll see that the mass is about 1 g. Obtaining the mass is simple enough. You whip the material up on the balance and read the display. Measuring the volume, however, ranges in difficulty. If it's a liquid, **how to solve dimensional analysis problems**, you *how to solve dimensional analysis problems* use a graduated cylinder.

If it's a solid then you have a couple of possibilities. If it's a geometric solid like a cube or a cylinder then you can take length measurements and, with the appropriate formula, calculate the volume. If it's an irregular solid, however, you need to use a different method. Let's look at each of the previous cases in turn before moving on to manipulating the density formula, *how to solve dimensional analysis problems*.

If you're given an unknown liquid with a mass of 3. Volumes for liquids are generally measured in mL, solids in cm 3and gases in L. However, remember that 1 mL is defined to be equivalent to 1 cm 3 so it's a snap to convert between the two. Let's try a solid.

What if you've got a rectangular solid? How do you get volume? Therefore, what's the density of a 8. Remember how to calculate volume. It's not always quite so simple to calculate the volume.

If you have what's called an "irregular" solid, then it's too complicated to meaure the volume. Think about trying to determine your volume. The way to get it is to use the Archimedes Principle. Imagine if you filled the bathtub with water up to the very brim. What would happen if you then got into the tub?

Water would overflow and the amount would be equal to your own volume. That's how we get the volume of irregular solids. You fill a container with water to a specific volume and then measure the change when you drop your object into the water.

Let's try it. A solid has a mass of 5. The volume of the water rises to What is the density of the solid? The conversion from mL to cm 3 was done at the end simply to show you how to do it by unit analysis.

Not all density problems want you to actually calculate density. The formula involves density, mass, and volume. If you are given any 2, you can get the third. So, just how do we go about solving for mass or for volume if we are given the other 2? Let's walk through the formula manipulation this one time to demonstrate it. Given density and volume, solve for mass. The cycle button will cycle you through the process until you've solved for mass.

Given density and mass, solve for volume. The cycle button will cycle you through the process until you've solved for volume. Whether you are solving for mass, density, or volume, *how to solve dimensional analysis problems*, you must keep careful watch over the units, **how to solve dimensional analysis problems**.

The common type of mistake in rearranging the density formula is not properly checking the units at the end. The same goes for volume. A material has a density of 0. What's the volume of the substance in cm 3?

What happened to the units? I'm not referring to the mL instead of cm 3 since it's a one-to-one ratio, **how to solve dimensional analysis problems** simple to convert between them I trust you! This is where unit analysis comes into play along with algebra and fractions. Don't make the mistake of assuming your units are correct. Understand how to check them in situations like these!

Here, let's check.

### Dimensional Analysis Tutorial: Part 7- Density Problems

Whether you are solving for mass, density, or volume, you must keep careful watch over the units. The common type of mistake in rearranging the density formula is not properly checking the units at the end. If you are looking for mass, your units must be in g and not 1/g. The same goes for volume. convert this using the conversion factor table. find the measure in kilometers and then find time in hours all on the same line. multiply EVERYTHING together. how to use dimensional analysis. multiply everything on the top and then divide it by the first number on the bottom then divide that by the second number on the bottom and so on. Solve one-step and multi-step problems using dimensional analysis and conversion factors Explain how to cancel out numerator and denominator units To unlock this lesson you must be a .