Chapter 2: Measurement & Problem Solving

pg. 24-38

LO: I can use unit conversions successfully in mathematic calculations.

Units of Measurement

• Two common systems: English & Metric (International System or SI).

Common Base Units• Meter (m) = length• Kilogram (kg) = mass• Seconds (s) = time

Metric Prefixes

• A numerical prefix that changes a number by powers of 10

ExamplesWhat is the meaning?• Kilometer =• Centimeter =• Decimal =

Scientific NotationPg. 26 of your text!

Unit Conversions

• Converting a given unit into a desired unit

ExamplesHow many feet (ft.) are in 194 centimeters (cm)?

How can we solve this problem?

Unit Conversions

Setting up ratios (comparing one unit to another) in order to convert a given unit into a

desired unit through multiplication.

Solution MapsA great way to

map out a problem so you know what you

need to do!

Solution Maps

Question: How many feet (ft.) are in 194 centimeters (cm)?

• How do we get from centimeters (cm) feet (ft.)?

Example Solution Maps

Question: How many laps should

you run to run 10.0 kilometers

(km)?

Note: Important conversion factors

are on the PDF “End Paper” tab.

Example Solution Maps

Question: How many

centimeters (cm) are in 72 miles?

Note: Important conversion factors

are on the PDF “End Paper” tab.

Unit Conversions

Things to Remember• Always write every number with its associated unit

• Identify your starting point (given unit) and devise a solution map towards what you must find (desired unit)

• Check sig figs last when doing your calculations

• Determine if your answer makes sense

Practice

Ex: How many hours are in 4.5 years?

Practice

Ex: Convert 5.89 x 107 µg to kg

Unit Conversions

What do I do when a unit conversion is raised to a power?• You must also raise the conversion factor to that power.

Unit Conversions

Question: How many cubic feet (ft3) are in 4102 cubic centimeters (cm3)?

Solution Map Solution

Density

What is Density?A ratio of an objects mass to its volume

How is it calculated?Density =_mass_ D = M Volume V

Density is…

…Thus density can be used as a conversion factor!

Density

Ex: Using density as a conversion factor

The density of aluminum is 2.70 g/mL. What is the volume in liters of 256 g of an aluminum sample?

Temperature (Kelvin vs. Celsius)

Kelvin: SI base unit of temperature. 0 K = Absolute zero all particles (atoms) no longer have energy (heat).

Changing between Kelvin & Celsius temperatureKelvin Celsius = Kelvin Temp – 273 = Celsius Temp

Celsius Kelvin = Celsius Temp + 273 = Kelvin Temp

Lesson Summary

• Rate your understanding of the lesson (1-4)

• Think about your learning concerning the following points What types of math computations were discussed in the

chapter and why are they important?

How do solution maps and carrying units help you arrive to a correct answer when doing unit conversions?