DIMENSIONAL ANALYSIS

Dimensional Analysis

Unit conversion using conversion factors

Conversion factor- a fraction based on a definition and equal to 1 Example:

Definition (from the prefixes chart) 1 cm = 0.01 m

Conversion factors possible: 1 cm 0.01 m0.01 m OR 1 cm

Intro

How long can you hold your breath?

Convert it to DAYS!

To Convert between Units

Convert from 5.8 m to cm1. Write your given: 5.8 m2. Write your definition (based on the

prefixes chart)- how are your units related?

1 cm = 0.01 m3. Setup your conversion factor like

this:

Converting between units- continued (still step 3) & Step 4- solve. Cancel

unit that occur on both the top and the bottom.

Conversion Factor

The larger number goes with the smaller unit

The smaller number goes with the larger unit

Examples of dimensional analysis

For significant figures, look at the original number, so the answer should be 15.9 cm.

The conversion factor should generally not be considered when determining significant figures because it is a definition, an exact value.

Exception- when you calculated the number to use in the conversion factor.

Examples of dimensional analysis Convert 2.6 km to mm

First- what is the desired unit? Answer- mm

Second- how to we get from km to mm? We know that 1 km = 1000 m We know that 1 m = 1000 mm

2.6 km( 1000 m )(1000 mm) = 2600000 m

1 km 1 m

More examples

1. 1 Mg = 1000 kg. Which of the following would be a correct conversion factor for this relationship? 1000. 1/1000. ÷ 1000. 1000 kg/1Mg.

3.3 Section Quiz

3.3 Section Quiz

2. The conversion factor used to convert joules to calories changes the quantity of energy measured but not

the numerical value of the measurement. neither the numerical value of the

measurement nor the quantity of energy measured.

the numerical value of the measurement but not the quantity of energy measured.

both the numerical value of the measurement and the quantity of energy measured.

3.3 Section Quiz

3. How many g are in 0.0134 g? 1.34 10–4

1.34 10–6

1.34 106

1.34 104