# Chapter 2 – Scientific Measurement

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Chapter 2 – Scientific Measurement
I. Units of 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 your value
given value

B. Percent Error % error = 2.94 %
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. % 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

C. Significant Figures Same object with different rulers:

C. Significant Figures 739 5085 2.60 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 Trailing zeros without a decimal point -- 2,500 739 5085 2.60

Counting Sig Fig Examples
C. Significant Figures Counting Sig Fig Examples 4 sig figs 3 sig figs 3. 5,280 3. 5,280 3 sig figs 2 sig figs

C. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g
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) = g 4 SF 3 SF 3 SF 324 g

C. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL
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 mL 7.85 mL 3.75 mL mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  7.9 mL  350 g

C. Significant Figures Calculating with Sig Figs (cont’d)
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

C. Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL)
4 SF 2 SF = g/mL  2.4 g/mL 2 SF g g  18.1 g 18.06 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 g 2 x g coefficient exponent

D. Scientific Notation 65,000 kg  6.5 × 104 kg
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!

D. Scientific Notation Practice Problems 7. 2,400,000 g 8. 0.00256 kg
 10-5 km  104 mm 2.4  106 g 2.56  10-3 kg km 62,000 mm

D. Scientific Notation Calculating with Sci. Notation
(5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EE EXP EE ENTER EXE 5.44 7 8.1 ÷ 4 = = 670 g/mol = 6.7 × 102 g/mol

D. Scientific Notation Practice Problems 4  1010 cm2 6.9  10-2 kg2
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) 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!

CH. 2 – MEASUREMENT II. Unit Conversions

A. SI Prefix Conversions
1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places. To the left or right?

A. SI Prefix Conversions
= 532 m = _______ km 0.532 NUMBER UNIT NUMBER UNIT

A. SI Prefix Conversions
Symbol Factor mega- M 106 kilo- k 103 BASE UNIT --- 100 deci- d 10-1 move left move right centi- c 10-2 milli- m 10-3 micro- 10-6 nano- n 10-9 pico- p 10-12

A. SI Prefix Conversions
0.2 1) 20 cm = ______________ m 2) L = ______________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km 32 45,000 0.0805

M V D = B. Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L
Combination of base units. Volume (m3 or cm3) length  length  length 1 cm3 = 1 mL 1 dm3 = 1 L D = M V Density (kg/m3 or g/cm3) mass per volume

C. Density Mass (g) Volume (cm3)

C. Density V = 825 cm3 M = DV D = 13.6 g/cm3 M = (13.6 g/cm3)(825cm3)
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

C. Density D = 0.87 g/mL V = M V = ? M = 25 g V = 25 g 0.87 g/mL
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 = g 0.87 g/mL V = 29 mL

III. Dimensional Analysis
CH. 2 – MEASUREMENT III. Dimensional Analysis Conversion Factors Problems

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

B. Dimensional Analysis
The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out

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.

C. Conversion Factors Example: 1 in. = 2.54 cm
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: in. = 2.54 cm Factors: 1 in and cm 2.54 cm in.

C. Conversion Factors 1. Liters and mL 2. Hours and minutes
Learning Check: Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers 1 L 1000 mL 1000 mL 1 L = 1 hr 60 min 1000 m 1 km

How many minutes are in 2.5 hours?
Conversion factor cancel 2.5 hr 1 x 60 min 1 hr = 150 min 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!

D. Dimensional Analysis Practice
You have \$7.25 in your pocket in quarters. How many quarters do you have? 4 quarters 7.25 dollars X = 29 quarters 1 dollar

E. Dimensional Analysis Practice
How many seconds are in 1.4 days? Plan: days hr min seconds 1.4 days x 24 hr x 60 min x 60 sec = day 1 hr min sec sec 1.2 x105 sec

D. Dimensional Analysis Practice
How many milliliters are in 1.00 quart of milk? qt mL 1.00 qt 1 L 1.057 qt 1000 mL 1 L = 946 mL

D. Dimensional Analysis Practice
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 1000 g 1 kg 1 cm3 19.3 g = 35 cm3

D. Dimensional Analysis Practice
5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? cm in 8.0 cm 1 in 2.54 cm = 3.1 in

D. Dimensional Analysis Practice
6) Roswell football needs 550 cm for a 1st down. How many yards is this? cm yd 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 3 ft = 6.0 yd

D. Dimensional Analysis Practice
7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? m pieces 1.3 m 100 cm 1 m 1 piece 1.5 cm = 86 pieces

D. Dimensional Analysis Practice
How many liters of water would fill a container that measures 75.0 in3? in3 L 75.0 in3 (2.54 cm)3 (1 in)3 1 L 1000 cm3 = 1.23 L

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