I II III I. Units of Measurement Chapter 2 – Scientific Measurement.

I

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I. Units of Measurement

Chapter 2 – Scientific Measurement

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

http://www.brainpop.com/science/scientificinquiry/precisionandaccuracy/

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.

100g/mL 1.36

g/mL 1.36g/mL 1.40error %

% error = 2.94 %

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

Same object with different rulers:


C. Significant Figures Counting Sig Figs

Digits from 1-9 are always significant. Zeros between two other sig figs are always

significant One or more additional zeros to the right of

both the decimal place and another sig digit are significant

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

4 sig figs

3 sig figs

3 sig figs

2 sig figs


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) = 324.103g

324 g

4 SF 3 SF3 SF


Calculating with Sig Figs (cont’d) Add/Subtract – The # with the lowest

decimal value determines the place of the last sig fig in the answer.

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g 7.9 mL 350 g

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g


Calculating with Sig Figs (cont’d) Exact Numbers do not limit the # of sig

figs in the answer.Counting 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

= 2.390625 g/mL

18.1 g

6. 18.9 g

- 0.84 g

18.06 g

4 SF 2 SF

2.4 g/mL2 SF

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

2.4 106 g

2.56 10-3 kg

0.000070 km

62,000 mm


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

4 1010 cm2

6.9 10-2 kg2

1.1 x 10-6

1.86 x 103

5.01 x 1022

Homework

Complete Worksheet “Using Measurements – Chapter 2”: due tomorrow!

II. Unit Conversions

CH. 2 – MEASUREMENT

A. SI Prefix Conversions

1. Find the difference between the

exponents of the two prefixes.

2. Move the decimal that many places.

To the leftor right?

=


NUMBERUNIT

NUMBER

UNIT

532 m = _______ km0.532


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 le

ft

mo

ve r

igh

t BASE UNIT --- 100


1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

0.2

0.0805

45,000

32

C. DensityM

ass

(g)

Volume (cm3)

Δx

Δyslope D

V

M

C. Density

An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.

GIVEN:

V = 825 cm3

D = 13.6 g/cm3

M = ?

WORK:

M = DV

M = (13.6 g/cm3)(825cm3)

M = 11,200 g

V

MD

C. Density

A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?

GIVEN:

D = 0.87 g/mL

V = ?

M = 25 g

WORK:

V = M D

V = 25 g

0.87 g/mL

V = 29 mLV

MD

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III. Dimensional Analysis

Conversion Factors

Problems

CH. 2 – MEASUREMENT

A. Vocabulary

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

B. Dimensional Analysis

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

“factored” out

g

B. Dimensional Analysis

Steps:

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 Factors

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

1. Liters and mL

2. Hours and minutes

3. Meters and kilometers

C. Conversion Factors

Learning Check:

1 L1000 mL

1 hr60 min

1000 m1 km

1000 mL1 L

=

Conversion factor

cancel

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

numbers!

How many minutes are in 2.5 hours?

2.5 hr

1 x 60 min

1 hr = 150 min

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

X = 29 quarters

D. Dimensional Analysis Practice

7.25 dollars1 dollar

4 quarters

How many seconds are in 1.4 days?

Plan: days hr min seconds1.4 days x 24 hr x 60 min x 60 sec =

1 1 day1 hr 1 min

E. Dimensional Analysis Practice

120960 sec 120000 sec

1.2 x105 sec


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

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


5) 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= 3.1 in

cm in


6) Roswell football 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


7) 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

m pieces

1 piece

1.5 cm


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


I II III I. Units of Measurement Chapter 2 – Scientific Measurement.

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