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**Chapter 3 Measurement Accuracy vs Precision Percent Error**

Significant Figures Scientific Notation Temperature Conversions Dimensional Analysis Conversion Factors SI Conversions

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

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**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

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**A. Accuracy vs. Precision**

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**B. Percent Error your value given value**

Indicates accuracy of a measurement your value given value

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**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 %

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**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

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**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

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**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

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**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

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**C. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL**

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 mL 7.85 mL 3.75 mL mL 7.85 mL 7.9 mL

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**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

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**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

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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 atoms 4.6 x atoms coefficient exponent

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**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!

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**D. Scientific Notation Practice Problems**

7. 2,400,000 g kg 10-5 km 104 mm 2.4 106 g 2.56 10-3 kg km 62,000 mm

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**D. Scientific Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) =**

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

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**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

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**Temperature Conversions**

CH. 3 - MEASUREMENT Temperature Conversions

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**A. Temperature Temperature**

measure of the average KE of the particles in a sample of matter

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**Temperature 298.15 298 41.85 298 Convert these temperatures:**

25oC = ______________K -15oF = ______________ K 315K = ______________ oC 288K = ______________ oF 298.15 298 41.85 298

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Measurement Dimensional Analysis

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**A. Problem-Solving Steps**

1. Analyze 2. Plan 3. Compute 4. Evaluate

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**B. 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

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**B. Dimensional Analysis**

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

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**B. Dimensional Analysis**

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.

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**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.

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**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!

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**C. Conversion Factors 1. Liters and mL 2. Hours and minutes**

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

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**D. SI Prefix Conversions**

1. Memorize the following chart. (next slide) Find the conversion factor(s). Insert the conversion factor(s) to get to the correct units. 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.

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**A. SI Prefix Conversions**

Symbol Factor tera- T 1012 giga- G 109 mega- M 106 kilo- k 103 hecto- h 102 deka- da 101 move left move right BASE UNIT --- 100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- 10-6 nano- n 10-9

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**A. SI Prefix Conversions**

= 532 m = _______ km 0.532 NUMBER UNIT NUMBER UNIT

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**D. SI Prefix Conversions**

1 T(base) = (base) = 1012 (base) 1 G(base) = (base) = 109 (base) 1 M(base) = (base) = 106 (base) 1 k(base) = (base) = 103 (base) 1 h(base) = 100 (base) = 102 (base) 1 da(base) = 10 (base) 1 (base) = 1 (base) 10 d(base) = 1 (base) 100 c(base) = 1 (base) 1000 m (base) = 1 (base) 106 µ(base) = µ(base) = 1(base) 109 n(base) = n(base) = 1(base) micro

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**D. SI Prefix Conversions**

1 m 100 cm a. cm to m b. m to µm c. ns to s d. kg to g 1 m 106 µm 1 s 109 ns 1 kg 1000 g

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**D. SI Prefix Conversions**

20 cm = ______________ m 2) L = ______________ mL 3) 45 m = ______________ m

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**D. SI Prefix Conversions**

4) 805 Tb = ______________ b Terabytes bytes 805 Tb 1 1012 b 1 Tb = 805 x 1012 bytes = 8.05 x 1014 bytes

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**D. SI Prefix Conversions**

5) 400. g = ______________ kg 6) 57 Mm = ______________ nm

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**E. Dimensional Analysis Practice**

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

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**E. Dimensional Analysis Practice**

2. How many seconds are in 1.4 days? Plan: days hr min seconds

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**E. Dimensional Analysis Practice**

3. How many milliliters are in 1.00 quart of milk?

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**E. 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.

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**E. Dimensional Analysis Practice**

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

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**E. Dimensional Analysis Practice**

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

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**E. 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?

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**E. Dimensional Analysis Practice**

8. How many liters of water would fill a container that measures 75.0 in3?

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