Factor-label Method

In math you use numbers, in chemistry we use quantities.

A quantity is described by a number and a unit.

100 is a number : 100 Kg is a quantity (notice that in chemistry we give meaning to the numbers). In science we solve a lot of the "math" by watching the units of the quantities

There are two main rules to solving science problems with the factor-label method:

1. Always carry along your units with any measurement you use.

2. You need to form the appropriate labeled ratios (equalities).

Example Problem:

How many centimeters in 2 meters?

You will see from the metric conversion chart that 1 meter = 100 cm

we turn this into a ratio by writing it like this:

or

Once you have the equalities you must pick the one that will cancel out the units leaving the desired units.

Then multiply your starting quantity (2 meters) by the equality that will give you your desired units.

As a rule of thumb your problem set up should look like this:

Practice Problems:

1. How many wheels on 350 Ford pickups (use the equality 1 pickup = 4 tires)

-the starting units are pickups, the ending units need to be wheels.

2. How many millimeters in 34 hectometers (use the equality 10,000 mm = 1 hectometer)?

Sometimes you will need to multiply by more than one ratio to get to your desired units, you can do this by using linking units. Your setup will look like this:

3. How many inches in 1 meter given the equality 1 inch = 2.54 cm and 1 meter = 100 cm? (note the linking unit in this problem is cm)

4. If a warehouse holds 3000 boxes, and a truck holds 235 boxes. How many truckloads will it take to fill up one warehouse?

5. How many grams in 150 pounds given the equalities 1 pound = 0.454 kg and 1 kg = 1000 grams?

## Solids, Liquids, Gases Compared

### Solids

The particles of a solid are always arranged in an orderly manner. They have a constant volume, because the particles are so closely packed together, with very little space between them. Compression of a solid to any large extent is not possible because of this tight pack of particles.

### Liquids

A fluid is any substance that flows, and liquids are examples of fluids. The particles in liquids are allowed to freely move and change their positions. At all times are the particles moving, moving from neighbor to neighbor. This is why we can 'pour' a liquid into another container. A liquids confinement are the borders of its container. This is why when we pour a liquid into another container, there is conformity to the shape of the container. Compression of a liquid to any large extent is not possible.

### Gases

Gases is another example of a fluid, it flows! The particles of gases are however much different than that of solids and liquids. The particles in gases are not neatly arranged, and they don't even touch each other most of the time. There is lots of space in between particles, which is why when put in a container, it is filled with the gas. And when released from a container, the gas is dispersed. The particles in gases are always moving, just like the particles in a liquid.

## Significant Digits

Number Digits to count Example Number of Significant Digits
Nonzero digits All *8341* 4
Leading Zeros None 0.000*79* 2
Captive zeros All *1200.00043* 9
Trailing Zeros Only if decimal point *400.0* and *4*00 4 and 1
Scientific Notation All *3.7* X 10-2 2

Rounding Fives with Significant Digits:

For a 5, even with zeros trailing it, increase the last significant digit (see above) by 1 if the digit preceding the 5 is odd. Do not change the last significant digit if the digit preceding the 5 is even. Take a look at these examples:

3.7500 becomes 3.8

3.6500 becomes 3.6

For a five followed by non-zero digits, just increase the last significant digit by 1.

8.652 becomes 8.7

8.6504 becomes 8.7