Chapter 4

List several useful problem solving skills Deductive reasoning Inductive reasoning

A three step problem solving approach, (ACE) Analyze Calculate Evaluate

Conversion Factors Must be constructed from

equivalent measurements Example: 1 dollar equals 4 quarters,

($1 = 4 x 25 cents) Equal in value

Example: 1 meter = 100 centimeters A small number of large items = a large

number of small items The meter stick has 100 cm or 1000

millimeters or 10 decimeters All are valid and equivalent measurements 100cm/1meter converts from meters to cm 1 meter/100 cm converts from cm to meters

Dimensional Analysis is a way to analyze and solve problems using the UNITS or dimensions of the measurements If each person at a party will eat 2

hamburgers, how many will you need for 18 people? 36 HB 2 HB/1 person x 18 person = 36 HB

If each HB has 2 pickles, how many will you need?

36 HB x 2 pickles/1 HB = 72 pickles If 1 jar of pickles has 110 pieces, how many

HB could be made?

Multi Step Problems Miles to Feet to Yards: If you went 3.5

miles, how many yards is that? What you need to know:

1 mile = 5280 feet 1 yard = 3 feet

How to convert, (the units miles and feet cancel) 3.5 miles x 5280 feet/1mile x 1yard/3

feet = ___ yards You get an answer in yards -> 6160 yards

Converting Complex Units Many measurements are expressed as a ratio of

units, (miles per hour, Kilometers per second,…) Convert 10 mi/hr to km/sec, (the units of same color

cancel)

10 mi/hr x 1 km/.55 mi x 1 hr /60 min x 1min / 60 sec=

So you are left with units of km/secThe math is 10 x 1 x 1 x 1 / .55 x 60 x 60

=The answer is 0.005 km/sec