I. Using Measurements MEASUREMENT

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

Accuracy - how close a measurement is to the accepted value

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

B. Percent Error Indicates accuracy of a measurement your value accepted value

Indicates accuracy of a measurement

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. % error = 2.9 %

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.

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 2.35 cm

Indicate precision of a measurement.

Recording Sig Figs

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

C. Significant Figures Counting Sig Figs Count all numbers EXCEPT: Leading zeros -- 0.00 25 Trailing zeros without a decimal point -- 2,5 00

Counting Sig Figs

Count all numbers EXCEPT:

Leading zeros -- 0.00 25

Trailing zeros without a decimal point -- 2,5 00

C. Significant Figures 4. 0.080 3. 5,280 2. 402 1. 23.50 Counting Sig Fig Examples 1. 23.50 2. 402 3. 5,28 0 4. 0.0 80 4 sig figs 3 sig figs 3 sig figs 2 sig figs

D. Scientific Notation 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. 65,000 kg  6.5 × 10 4 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.

D. Scientific Notation 7. 2,400,000  g 8. 0.00256 kg 9. 7  10 -5 km 10. 6.2  10 4 mm Practice Problems 2.4  10 6  g 2.56  10 -3 kg 0.00007 km 62,000 mm

7. 2,400,000  g

8. 0.00256 kg

9. 7  10 -5 km

10. 6.2  10 4 mm

D. Scientific Notation Calculating with Sci. Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 ÷ 7 8.1 4 = 671.6049383 = 670 g/mol = 6.7 × 10 2 g/mol Type on your calculator: EXP EE EXP EE ENTER EXE

Calculating with Sci. Notation

E. Proportions Direct Proportion Inverse Proportion y x y x

Direct Proportion

Inverse Proportion

II. Units of Measurement MEASUREMENT

A. Number vs. Quantity Quantity - number + unit UNITS MATTER!!

Quantity - number + unit

B. SI Units Quantity Base Unit Abbrev. Length Mass Time Temp meter kilogram second kelvin m kg s K Amount mole mol Symbol l m t T n

B. SI Units Prefix Symbol Factor mega- M 10 6 deci- d 10 -1 centi- c 10 -2 milli- m 10 -3 micro-  10 -6 nano- n 10 -9 pico- p 10 -12 kilo- k 10 3 BASE UNIT --- 10 0

C. Derived Units Combination of base units. Volume (m 3 or cm 3 ) length  length  length 1 cm 3 = 1 mL 1 dm 3 = 1 L Density (kg/m 3 or g/cm 3 ) mass per volume D = M V

Combination of base units.

Volume (m 3 or cm 3 )

length  length  length

Density (kg/m 3 or g/cm 3 )

mass per volume

Measuring Pi Circumference (cm) Diameter (cm)

Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

1. Analyze

2. Plan

3. Compute

4. Evaluate

D. Density An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3 . Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,200 g

An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3 . Find its mass.

D. 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 V = 29 mL WORK : V = M D 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?

III. Unit Conversions 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 left or right?

1. Find the difference between the exponents of the two prefixes.

2. Move the decimal that many places.

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

A. SI Prefix Conversions Prefix Symbol Factor move left move right mega- M 10 6 deci- d 10 -1 centi- c 10 -2 milli- m 10 -3 micro-  10 -6 nano- n 10 -9 pico- p 10 -12 kilo- k 10 3 BASE UNIT --- 10 0

A. SI Prefix Conversions 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45  m = ______________ nm 4) 805 dm = ______________ km 0.2 0.0805 45,000 32

1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45  m = ______________ nm

4) 805 dm = ______________ km

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

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.

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.

B. Dimensional Analysis 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 =

Lining up conversion factors:

B. Dimensional Analysis How many milliliters are in 1.00 quart of milk? ( 1.057 qt = 1L ) 1.00 qt 1 L 1.057 qt = 946 mL 1000 mL 1 L qt mL 

How many milliliters are in 1.00 quart of milk? ( 1.057 qt = 1L )

B. Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3 . 1 kg = 2.2 pounds 1.5 lb 1 kg 2.2 lb = 35 cm 3 1000 g 1 kg 1 cm 3 19.3 g lb cm 3

You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3 .

1 kg = 2.2 pounds

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

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

B. Dimensional Analysis 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 = 3.2 in cm in

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

B. Dimensional Analysis 6) Taft football needs 550 cm for a 1st down. How many yards is this? 12 inches = 1 foot 3 feet = 1 yard 550 cm 1 in 2.54 cm = 6.0 yd 1 ft 12 in 1 yd 3 ft cm yd

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

12 inches = 1 foot 3 feet = 1 yard

B. Dimensional Analysis 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 1 piece 1.5 cm cm pieces

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