UNIT II.1Unit Conversions

II.1 UNIT CONVERSIONS

You MUST learn and use the unit conversion method (not your own method!)

A CONVERSION FACTOR: is a fractional expression relating or connecting two different units.

II.1 UNIT CONVERSIONS Example 1: There are 60 seconds in 1

minute. In statement form, 1 min = 60 sec

Conversion Factors:

The conversion factor relates 2 units (minutes to seconds).

II.1 UNIT CONVERSIONS

Example 2: $1.44 per dozen eggs.

Conversion Factors:

Conversion factors do not change the VALUE of something, they just change the UNITS.

To change the UNITS, multiply by the CONVERSION FACTOR.

II. 1 UNIT CONVERSIONS

THE UNIT CONVERSION METHOD:

We need 3 important pieces of information: unknown amount and units initial amount and units conversion factor (relating the initial units to

units of unknown)

II. 1 UNIT CONVERSIONS

o Example 3: How many seconds are in 20 minutes?

  Unknown amount: Initial amount: Conversion factor:

Solution

** ALWAYS include UNITS in your calculations!

II.1 UNIT CONVERSIONS

o Example 4: If a car can go 90km in 1 h, how far can the car go in 6.5 h?

Unknown amount: Initial amount: Conversion factor:

Solution

II.1 UNIT CONVERSIONS

o Example 5: If the price of gas is $1.10 per liter (l), how much will it cost to fill a 40 liter tank?

Unknown amount: Initial amount: Conversion factor:

Solution

II.1 UNIT CONVERSIONS

HOW TO PUT EVERYTHING TOGETHER

The general form of a unit conversion calculation is:

(Unknown amount) = ( Initial amount) x (Conversion factor)

II.1 UNIT CONVERSIONS

o Example 6 a. If 0.200 mL of gold has a mass of 3.86 g, what is the mass of 5.00 mL of gold?

Unknown amount: Initial amount: Conversion factor:  Solution

II.1 UNIT CONVERSIONS

*Important: Always ask yourself “which way do I have to write the conversion factor so that my units cancel properly?”

b. If 0.200 mL of gold has a mass of 3.86 g, what is the volume occupied by 100.0 g of gold?

  Unknown amount: Initial amount: Conversion factor:

Solution

II.1 UNIT CONVERSIONS

SUMMARY Identify unknown amount and its units (put

on left side of = sign). Identify the initial amount and its units (put

on right side of = sign). 3. Identify conversion factor. (Multiply initial

amount by conversion factor in such a way that one of the units cancel. You want to be left with units of unknown amount!)

4. Complete the problem by multiplying and/or dividing amounts of RHS.

ASSIGNMENT

II.1 UNIT CONVERSIONS

Multiple Unit Conversions  We can solve problems that require more than

one conversion factor.

o Example: If eggs are $1.44 per dozen, and if there are 12

eggs in a dozen, how many individual eggs can be bought for $4.32?

ANALYZE THE PROBLEM:

Unknown amount: Initial amount: Conversion factors:

II.1 UNIT CONVERSIONS

Solution: we require the connection conversion factor 1 gives the connection:

conversion factor 2 gives the connection:

Combining conversion factors 1 and 2 gives:

II.1 UNIT CONVERSIONS

Solve for unknown amount:

Unknown amount = Initial amount x Conversion factors (1 and 2)

ASSIGNMENT