12
Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Embed Size (px)

Citation preview

Page 1: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Dimensional Analysis II

Beyond Simple Conversion Problems: Identifying the GIVEN andthe DESIREDin Word Problems

Page 2: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Basic Steps in Dimensional Analysis

• Identify the GIVEN value/quantity.

• Identify the DESIRED value/quantity.

• Identify the CONVERSION FACTOR(S).• Set up the problem with the GIVEN first and the DESIRED last--

this will just be a blank space with an attached unit or units.

• Put in “bridging” conversion factors which will cancel units UP/DOWN such that the DESIRED unit(s) will come through un-cancelled.

• Do the math: multiply factors together that are in the numerators and divide by factors that are in the denominators.

Page 3: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Identification Clues• The GIVEN is usually a number all by

itself with no implied equality with something else.

• The DESIRED has a question word associated with it: How many, How much, What is the total cost, etc.

• CONVERSION FACTORS are (1) a pair of numbers with explicit or implicit equality or (2) an explicit “something per something.”

Page 4: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Setting Up the Problem

GIVEN CONV. CONV. CONV. DESIRED

FACTOR

FACTOR

FACTOR

2.000 GALS.

4 QTS.1

LITER1000 mL

1 GAL.1.057 QTS.

LITER

7569 mL

Convert 2.000 gallons to milliliters.

Page 5: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Ruth wanted to raise sheep on 8.1 acres of property. If it takes 0.125 hectare to raise one sheep, how many sheep can be raised on the property. There is one hectare per 2.47 acres.

Given:

Desired:

Conversion(s)

8.1 acres

How many sheep?

0.125 hectare per sheep1.0 hectare per 2.47 acres

Page 6: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Given Conversion Factors Desired

8.1 ÷ 2.47 ÷ 0.125 = 26 sheep

8.1 acres hectare 1 sheep = sheep

2.47 acres

0.125 hectare

Page 7: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

A fast food worker wraps 350 hamburgers every hour. He works 8 hours per day. He works 5 days a week. He gets paid every 2

weeks with a salary of $440.34 (after taxes). How many hamburgers will he have to wrap to

make his first one million dollars?

Given:

Desired:

Conversion(s)

$1,000,000

How many hamburgers?

$440.34 per 2 weeks5 days per week8 hours per day350 burgers per hour

Page 8: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Given Conversion(s) Desired

1,000,000 x 2 x 5 x 8 x 350 ÷ 440.34 =

63.6 million hamburgers wrapped

(63,600,000)

$1,000,000 2 wks. 5 days

8 hours

350 HB = HB

$440.34

wk day hour

Page 9: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

How many ounces in 54 grams? (There are 16 ounces per 454 g).

16 ounces

454 g

Given:

Desired:

Conversion(s)

54 grams

How many ounces?

16 ounces per 454 g

Page 10: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Given Conversion(s)

Desired54 Grams 16 ounces = ounces

454 grams

54 x 16 ÷ 454 = 1.90 ounces

Page 11: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

If you are going 50 miles per hour, how many feet per second are you traveling? (5280 feet per mile). In this problem, the GIVEN looks the same as a CONVERSION FACTOR. It makes it harder to identify!!

5280 Feet

Mile

Given:

Desired:

Conversion(s)

50 miles per hour

How many feet per sec?

5280 feet per mile, and you should know the ones for time.

Page 12: Dimensional Analysis II Beyond Simple Conversion Problems: Identifying the GIVEN and the DESIRED in Word Problems

Given Conversion(s) Desired

50 x 5280 ÷ 60 ÷ 60 = 73.3 Ft per Sec

50 Miles

5280 Ft. Hour Min = Feet

Hour Mile 60 Min 60 Sec Sec