I II III Units of Measurement Scientific Measurement

I

II

III

Units of Measurement

Scientific Measurement

August 20th – 2nd, 3rd, 6th Periods August 21st – 6th, 7th Periods

Number vs. Quantity

Quantity - number + unit

UNITS MATTER!!

A. Accuracy vs. Precision

Accuracy - how close a measurement is to the accepted value

Precision - how close a series of measurements are to each other

ACCURATE = CORRECT

PRECISE = CONSISTENT

A. Accuracy vs. Precision

B. Percent Error

Indicates accuracy of a measurement

100accepted

acceptedalexperimenterror %

your value

given value

B. Percent Error

A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

2.94%

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

C. Significant Figures

Indicate precision of a measurement.

Recording Sig Figs

Sig figs in a measurement include the known digits plus a final estimated digit

2.31 cm

C. Significant Figures Counting Sig Figs

Digits from 1-9 are always significant

Zeros between two other sig figs are always significant

Zeros at the end of a number are significant when a decimal is present

Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without

a decimal point -- 2,500

5085

2.60

739

4. 0.080

3. 5,280

2. 402

1. 23.50


Counting Sig Fig Examples

1. 23.50

2. 402

3. 5,280

4. 0.080


Calculating with Sig Figs

Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer

(13.91g/cm3)(23.3cm3) =


Calculating with Sig Figs (con’t) Add/Subtract – Answer can have as

many # after the decimal as the # with the least amount of # to the right of the decimal

3.75 mL

+ 4.1 mL

7.85 mL

3.75 mL

+ 4.1 mL

7.85 mL


Calculating with Sig Figs (con’t)

Exact Numbers do not limit the # of sig figs in the answerCounting numbers: 12 studentsExact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm


5. (15.30 g) ÷ (6.4 mL)

Practice Problems

6. 18.9 g

- 0.84 g

August 21st – 2nd, 3rd periods August 22nd- 5th, 6th, 7th periods

D. Scientific Notation

A way to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to a power (exponent)

Number of carbon atoms in the Hope diamond

460,000,000,000,000,000,000,000

4.6 x 1023

Mass of one carbon atom

0.00000000000000000000002 g

2 x 10-23 g coefficient exponent


Converting into Sci. Notation:

Move decimal until there’s 1 digit to its left. Places moved = exponent

Large # (>1) positive exponentSmall # (<1) negative exponent

Only include sig figs – all of them!

65,000 kg 6.5 × 104 kg


7. 2,400,000 g

8. 0.00256 kg

9. 7.0 10-5 km

10. 6.2 104 mm

Practice Problems


Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:


11. (4 x 102 cm) x (1 x 108cm)

12. (2.1 x 10-4kg) x (3.3 x 102 kg)

13. (6.25 x 102) ÷ (5.5 x 108)

14. (8.15 x 104) ÷ (4.39 x 101)

15. (6.02 x 1023) ÷ (1.201 x 101)

Practice Problems

August 26th- 2nd, 3rd, 5th, 6th, 7th periods

Temperature

Conversions

CH. 3 - MEASUREMENT

A. Temperature

Temperature measure of the average

KE of the particles in a sample of matter

273.15Kelvin Co

32Fahrenheit Co 5

9

32)Celsius F( 9

5 o

Convert these temperatures:

1) 25oC = ______________K

2) -15oF = ______________ K

3) 315K = ______________ oC

4) 288K = ______________ oF

A. Temperature

I

II

III

Dimensional Analysis

Conversion Factors

Problems

CH. 3 - MEASUREMENT

A. Problem-Solving Steps

1. Analyze

2. Plan

3. Compute

4. Evaluate

B. Dimensional Analysis

Dimensional Analysis A tool often used in science for

converting units within a measurement system

Conversion Factor A numerical factor by which a quantity

expressed in one system of units may be converted to another system

3

3

cm

gcm


The “Factor-Label” Method Units, or “labels” are canceled, or

“factored” out

g


Steps to solving problems:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

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

4. Check units & answer.

Fractions in which the numerator and denominator are EQUAL quantities expressed in different units

Example: 1 in. = 2.54 cm

Factors: 1 in. and 2.54 cm

2.54 cm 1 in.

C. Conversion FactorsC. Conversion Factors

Conversion factor

cancel

By using dimensional analysis / factor-label method, By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the side up, and the UNITS are calculated as well as the

numbers!numbers!

How many minutes are in 2.5 hours?

2.5 hr2.5 hr

1 1

x x 60 min60 min

1 hr

= 150 min

Write conversion factors that Write conversion factors that relate each of the following pairs relate each of the following pairs of units:of units:

1. Liters and mL1. Liters and mL

2. Hours and minutes2. Hours and minutes

3. Meters and kilometers3. Meters and kilometers

C. Conversion Factors

Learning Check:

D. SI Prefix Conversions

1. Memorize the following chart. (next slide)

2. Find the conversion factor(s).

3. Insert the conversion factor(s) to get to the

correct units.

4. When converting to or from a base unit, there

will only be one step. To convert to or from any

other units, there will be two steps.

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

kilo- k 103

BASE UNIT --- 100

giga- G 109

deka- da 101

hecto- h 102

tera- T 1012

mo

ve le

ft

mo

ve r

igh

tA. SI Prefix Conversions

pico- p 10-12


1 T(base) = 1 000 000 000 000(base) = 1012 (base)

1 G(base) = 1 000 000 000 (base) = 109 (base)

1 M(base) = 1 000 000 (base) = 106 (base)

1 k(base) = 1 000 (base) = 103 (base)

1 h(base) = 100 (base) = 102 (base)

1 da(base) = 101 (base)

1 (base) = 1 (base)

10 d(base) = 1(base)

100 c(base) = 1 (base)

1000 m (base) = 1(base)

1 (base) = 1 000 000 µ = 10-6(base)

1 (base) = 1 000 000 000 n = 10-9(base)

1 (base) = 1 000 000 000 000 p = 10-12(base)

Tera-

Giga-

Mega-

Kilo-

Hecto-

Deka-

Base

Deci-

Centi-

Milli-

Micro-

Nano-

Pico-

a. cm to m

b. m to µm

c. ns to s

d. kg to g



1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ m

4) 805 Tb = ______________ b

Terabytes bytes


1) 400. g = ______________ kg

1) 57 Mm = ______________ nm


You have $7.25 in your pocket in You have $7.25 in your pocket in quarters. How many quarters do quarters. How many quarters do you have?you have?

X

E. Dimensional Analysis Practice

7.25 dollars7.25 dollars

11 1 dollar1 dollar4 quarters4 quarters

How many seconds are in 1.4 days?

= 12000 s


1.4 days

24 hr 60 min

60 s

1 day

1 hr 1 min


How many milliliters are in 1.00 quart of milk?

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


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


6) Roswell football needs 550 cm for a 1st down. How many yards is this?


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


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


Documents

I II III Units of Measurement Scientific Measurement