 # Unit 2. Measurement This lesson is 8 days long.

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Unit 2. Measurement This lesson is 8 days long

Do Now In your own words, what do you think is the difference between:
Accuracy and Precision?

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

ACCURATE = CORRECT PRECISE = CONSISTENT

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

B. Percent Error % error = 2.90 %
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 = 2.90 %

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

C. Significant Figures 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 2.35 cm

C. Significant Figures Count all numbers EXCEPT:
Counting Sig Figs (Table 2-5, p.47) Count all numbers EXCEPT: Leading zeros (not significant) Trailing zeros without a decimal point -- 2,500 (not Significant) Zeros between numbers are significant

Counting Sig Fig Examples
C. Significant Figures Counting Sig Fig Examples 3. 5,280 3. 5,280

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 Calculating with Sig Figs Multiply/Divide –
The # with the fewest sig figs determines the # of sig figs in the answer.

Multiplication and Division Rules
Do the sum Round the answer to the least significant figure in the problem 13.91g/cm3)(23.3cm3) = g 4SF 3SF 3SF 324g

C. Significant Figures 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.

Stack the numbers so that the decimal point is aligned Do the sum Figure out which number has least decimal place (least precise/decimal area least far out) Draw a line after the last number with the least decimal place Round the digit by looking at the number that follows

Example mL mL mL  7.9 mL

C. Significant Figures 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

Practice Problems - 0.84 g 18.06 g 5. (15.30 g) ÷ (6.4 mL) 4 SF 2 SF

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.

Practice Problems D. Scientific Notation 7. 2,400,000 g 8. 0.00256 kg
9. 7  10-5 km  104 mm

Practice Problems D. Scientific Notation 2.4  106 g 7. 2,400,000 g
kg 9. 7  10-5 km  104 mm 2.56  10-3 kg km 62,000 mm

D. Scientific Notation Type on your calculator: = 671.6049383
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

E. Proportions Direct Proportion y x Inverse Proportion y x

Units of Measurement

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

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

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

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

D. Density Mass (g) Volume (cm3)

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

D. Density V = 825 cm3 D = 13.6 g/cm3 M = ? GIVEN: WORK:
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:

D. 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

D. Density D = 0.87 g/mL V = ? M = 25 g GIVEN: WORK:
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:

D. 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. 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
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
1) 20 cm = ______________ m 2) L = _____________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km

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 C. Johannesson

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 bottom number. 4. Check units & answer.

B. Dimensional Analysis
Lining up conversion factors: ARE THESE THE SAME? = 1 1 in = 2.54 cm 2.54 cm cm 1 = 1 in = 2.54 cm 1 in in

B. Dimensional Analysis
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

B. Dimensional Analysis
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

B. Dimensional Analysis
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

B. Dimensional Analysis
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 = 3.2 in

B. Dimensional Analysis
6) Taft 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

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? cm pieces 1.3 m 100 cm 1 m 1 piece 1.5 cm = 86 pieces