1

1.7 Problem Solving

2

A ratio derived from A ratio derived from the equality between the equality between two different units two different units that can be used to convert that can be used to convert from one unit to anotherfrom one unit to another

Conversion Factors

3

Conversion factors always equal 1.Conversion factors always equal 1. The numerator is equal to the The numerator is equal to the

denominator.denominator.

Conversion Factors

4 quarters1 dollar

= 1

12 inches1 foot

= 1

1 kilogram1000

grams

= 1

4

Convers

ion F

act

ors

A

nim

ati

on

5

A mathematical techniqueA mathematical techniquethat allows you to use unitsthat allows you to use unitsto solve a problem to solve a problem involving measurementsinvolving measurements

Dimensional Analysis

6

Dimensional Analysis

# given unit

xwanted

unitgiven unit= # wanted unit

Put in numbers to make the numerator

equal to the denominator

7

Dimensional Analysis

x x x x =

Arrange the units so that all cancel out except the last one, which should be the one you want.

8

Using Conversion Factors Imagep.

40*

p. 4

0*

9

Dimensional Analysis How many seconds in one week?How many seconds in one week?

10

Dimensional Analysis1.1. Express a length of 16.45 m in Express a length of 16.45 m in

centimeters and in kilometers.centimeters and in kilometers.

2.2. Express a mass of 0.014 mg in grams.Express a mass of 0.014 mg in grams.

p. 4

0

1. 1645 cm and 0.01645 km 2. 0.000 014 g

11

10um x10um x  1m     1m   x  x  39.37inches39.37inches = = 0.0003937in0.0003937in

             1,000,000um   1m  1,000,000um   1m    

                                 

12

Practice Problems

250.cm to inches250.cm to inches ? gal in 39L? gal in 39L ? cm in 16in? cm in 16in ? seconds in 5 days? seconds in 5 days ? ft in 86cm? ft in 86cm ? cm3 in 2.3gal? cm3 in 2.3gal ? m in 3.5mi? m in 3.5mi

13

Direct Proportions Two quantities are directly proportional Two quantities are directly proportional

to each other if dividing on by the other to each other if dividing on by the other gives a constant valuegives a constant value

As Y increases; X increasesAs Y increases; X increases

Y X

= k Y = k XThe equation for a

line!k is the slope.

14

Directly Proportional Graphp.

55

p. 5

5

The line must go through the origin to be directly proportional

15

Inverse Proportions Two quantities are inversely proportional Two quantities are inversely proportional

to each other if their product is constant.to each other if their product is constant. As X increases; Y decreasesAs X increases; Y decreases

X Y = k X Y = k

produces a curve – a hyperbolaproduces a curve – a hyperbola

16

Inversely Proportional Graphp.

57

p. 5

7

17

Dir

ect

ly P

roport

ional &

Invers

ely

Pro

port

ional

Gra

ph A

nim

ati

on