Units of Measurement - Eagle...

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III

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

A. Accuracy vs. Precision

B. Percent Error

Indicates accuracy of a measurement

100accepted

alexperimentacceptederror %

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 1.401.36g/mLerror %

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


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


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 - 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

3.75 mL

+ 4.1 mL

7.85 mL

224 g

+ 130 g

354 g


Calculating with Sig Figs (con’t)

Exact Numbers do not limit the # of sig

figs in the answer

Counting numbers: 12 students

Exact 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

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 exponent

Small # (<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) =

5.44 EXP

EE ÷

EXP

EE ENTER

EXE 7 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

Temperature

Conversions

CH. 3 - MEASUREMENT

A. Temperature

Temperature

measure of the average

KE of the particles in a

sample of matter

273Kelvin 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

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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 Factors

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

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:

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

t A. 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) = 10 (base) = 101 (base)

1 (base) = 1 (base)

1 d(base) = 0.1 (base) = 10-1 (base)

1 c(base) = 0.01 (base) = 10-2 (base)

1 m (base) = 0.001 (base) = 10-3(base)

1 µ(base) = 0.000 0001 (base) = 10-6(base)

1 n(base) = 0. 000 000 0001 (base) = 10-9(base)

1 p(base) = 0.000 000 000 0001 (base) = 10-12(base)

The

Great

Man

King

Henry

Died

By

Drinking

Chocolate

Milk

Monday

Night

Partying

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


Homework

Complete Worksheet “Using

Measurements – Chapter 3”:

due tomorrow!

You have $7.25 in your pocket in

quarters. How many quarters do

you have?

X

E. Dimensional Analysis Practice

7.25 dollars

1 1 dollar

4 quarters

How many seconds are in 1.4 days?



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?


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