I

II

III

Measurement

&

Dimensional Analysis

Learning Objective

The Learners Will (TLW) express and manipulate chemical quantities using scientific conventions and mathematical procedures such as measurement conversion and dimensional analysis

TEKS 2.G.

Agenda

Part 3 – Measurement Conversions Reviewed

A. SI Prefix Conversions –

Shorthand Method

B. Dimensional Analysis –

The “Factor-Label Method” of

solving problems

I

II

III

Unit Conversions

MEASUREMENT

A. SI Prefix Conversions

mega- M 106

deci- d 10-1

centi- c 10-2

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

nano- n 10-9

pico- p 10-12

kilo- k 103

mo

ve d

ecim

al le

ft

Mo

ve d

ecim

al r

igh

t

BASE UNIT l,m,g 100

Scientific Notation

is Back!!!!!!!!

A. SI Prefix Conversions

1. Find the absolute difference between

the exponents of the two prefixes

2. Move the decimal that many places

To the leftor right?

If going from larger factor to smaller, move decimal to right

If going from smaller factor to larger, move decimal to left

=

A. SI Prefix Conversions

NUMBERUNIT

NUMBER

UNIT

532 m = _______ km0.532

A. SI Prefix Conversions

YOUR TURN

1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

0.2

0.0805

45,000

32

Practice Set

1) 5 cm = ______________ mm

2) 0.006 L = ______________ kL

3) 40 m = ______________ nm

4) 750 m = ______________ km

5) 50,000 g = ______________ kg

B. Dimensional Analysis

You might not recognize the fancy name, but you do use it every day

For example – Making change for a dollar bill in dimes Converting how many minutes until this

boring class ends into seconds Determining how many teaspoons of

medicine to take to equal two tablespoons

3

3

cm

gcm

B. Dimensional Analysis

Also called the “Factor-Label” Method Units, or “labels” are canceled, or

“factored” out

g

B. Dimensional Analysis

Steps:

1. Identify starting & ending numbers and associated units (labels).

2. Line up conversion factors so units (labels) cancel. This may mean inverting or doing the butterfly.

3. Multiply all top numbers & divide by each bottom number.

4. Check units & answer.

B. Dimensional Analysis

Step 1: What are known factors and units? What conversion factors do you have, know, or

need? What are you solving for?

You have a belt that is 40 inches long. How long is it in centimeters?

Starting = 40 inches Ending = x cm

Conversion factor 2.54 cm per inch or 2.54 cm

1 in.

B. Dimensional Analysis

Step 2: Lining up conversion factors:

1 in = 2.54 cm

2.54 cm 2.54 cm

1 in = 2.54 cm

1 in 1 in

= 1

1 =

In a word problem, think of the word “per” as the fraction line.

If conversion factor is written as 2.54 cm = 1 in., think of “equals sign” as fraction line

B. Dimensional Analysis

Step 3: Multiply all top numbers & divide by each bottom number

inches cm

40 inches 2.54 cm

1 in= 101.6 cm

B. Dimensional Analysis

Step 4: Check units and answer

We have cm and our math looks good

B. Dimensional Analysis

1.How many milliliters are in 1.00 quart of milk?

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L

B. Dimensional Analysis

2. You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g

B. Dimensional Analysis

3. How many liters of water would fill a container that measures 75.0 in3?

75.0 in3 (2.54 cm)3

(1 in)3= 1.23 L

in3 L

1 L

1000 cm3

B. Dimensional Analysis

4. Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm 1 in

2.54 cm= 3.2 in

cm in

B. Dimensional Analysis

5. Industrial’s football team needs 550 cm for a 1st down. How many yards is this?

550 cm 1 in

2.54 cm= 6.0 yd

cm yd

1 ft

12 in

1 yd

3 ft

B. Dimensional Analysis

6. A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

1.3 m 100 cm

1 m= 86 pieces

cm pieces

1 piece

1.5 cm

B. Dimensional Analysis

A very useful technique for solving complex conversion problems, especially in engineering, chemistry, physics, medicine

B. Dimensional Analysis

Review the Steps to Using Dimensional Analysis

More practice as a group and as individuals – Problem Sets

Chemistry Textbook – page 95, problems 15 – 19

Dimensional Analysis Problem Set