Tools of Chemistry Measurement Scientific Method Lab Safety & Apparatus
Scientific Notation Scientific Notation a number described as a power of 10 (used for very large or small numbers) 1000 = 1 X 10 X 10 X10 = 1 X 10 3 Format: M x 10 n or M E n
Expanded to Scientific Remember, M x 10 n Notation Step 1: To find M, find the place within the value where if a decimal were placed it would be a number between 1 and 10 Ex: 14 M = 1.4
Expanded to Scientific Notation Step 2: Count how many places you have to move decimal to reach this position (this is the n) For numbers >1 the superscript is + For numbers <1 the superscript is Ex: 14, where M = 1.4 Need to move decimal 1 place, so n = 1 14 in scientific notation: 1.4 x 10 1
Practice 0.005 0.25 5,050 0.025 0.0008 0.0025 1,000 500 1,000,000 5,000
Scientific Notation to Expanded Remember that M x 10 n, where: 1 < M > 10 n tells how many times to move the decimal - to the left + to the right
Practice 1.5 x 10 3 3.35 x 10-1 1.5 x 10-3 1.2 x 10-4 3.75 x 10-2 1 x 10 4 3.75 x 10 2 1 x 10-1 2.2 x 10 5 4 x 10 0 Keep going Q s 1-16 on sheet
kilo- K kg km kl hecto- H D hg hm hl giga- 10 9 G- mega- 10 6 M- micro- 10-6 u- nano- 10-9 n- pico- 10-12 p- deka- dag dam dal BASE B GRAM METER LITER deci- D centidg C millidm dl cg M cm cl King Henry Doesn t Bother Doing Common Math mg mm ml
Must Know Prefixes! kilo- 1000 m = 1 km centi- 1 m = 100 cm milli- 1 m = 1000 mm
Measurement Measurement a quantity that has both a number and a unit (ex: 4 grams) Scientists use the metric system (SI units) when reporting data NASA
Common SI Units Measurement Unit Symbol Length Mass Volume Temperature Time # of Particles Energy Meter Gram Liter Kelvin Second Mole Joule m g L K s mol J
Making Measurements Determine the scale of the instrument Always estimate 1 digit beyond scale on instrument Degree of uncertainty is always +/- 1 of the last digit
Making Measurements
In the measurement 0.503 L, which digit is the estimated digit? A.) 5 B.) the 0 immediately to the left of the 3 C.) 3 D.) the 0 to the left of the decimal point
Practice 0 1 2 3 4 5 6 7cm How much distance is represented by each increment? What is the measurement reading?
A.) 40.3 ml B.) 43 ml C.) 43.0 ml D.) 43.00 ml
Significant Figures A measurement that includes all of the digits that are known, plus a last digit that is estimated Atlantic-Pacific Rule P A C I F I C A T L A N T I C
Atlantic-Pacific Rule If decimal Present, start from Pacific side (L) The count begins with the first nonzero, all digits that follow are significant Ex: 0.0978 0.0978 3 significant digits
Atlantic-Pacific Rule If decimal Absent, start from Atlantic side (R) The count begins with the first nonzero, all digits that follow are significant Ex: 73,000 Ex: 73,000 2 significant digits
Practice 0.02 0.020 501 501.0 5,000 5,000. 6,051.00 0.0005 0.1020 10,001
How many significant figures are in the measurement 811.40 grams? A.) 2 B.) 3 C.) 4 D.) 5
How many significant figures are in the measurement 40,500 mg? A.) 2 B.) 3 C.) 4 D.) 5
How many significant figures are in the measurement 0.0034 kg? A.) 1 B.) 2 C.) 4 D.) 5
Rounding Find the last significant or decimal value allowed. Look at the digit that follows. If the next number is 5 or greater round up. If the number is less than 5 leave preceding digit alone. Fill in zeros to mark the size
What is the measurement 111.009 mm rounded off to four significant digits? A.) 111 mm B.) 111.0 mm C.) 111.01 mm D.) 110 mm
Significant Figures in Calculations Multiplication and Division the answer should contain as many significant figures as the least precise measurement
Practice 2.698 x 33.20 x 1.5611 = 124.2848 8.032 / 0.591 = 13.5905 (3.2 x 103)(4.21 x 102) = 1347200 (2.5000 x 106)(3.92 x 10-3) = 10525 3 x 154 = 462
Addition and Subtraction the answer should contain as many decimal places as the measurement with the smaller number of decimal places T H O U S A N D S H U N D R E D S T E N S O N E S T E N T H S H U N D R E D T H S T H O U S A N D T H S Significant Figures in Calculations
Practice 11) 7.623 + 85.0 + 9.815 = 102.4380 12) 230.72 + 0.00861 = 230.72861 13) 10.96 5.5 = 5.4600 14) 10.96-5.555 = 5.405 15) 9.0731 + 0.00078 = 9.0739
Practice 1) 1.35 x 2.467 = 3.33045 9) 1.252 x 0.115 x 0.012 = 0.001727 2) 1,035 / 42 = 24.6428 10) (1.278 x 103)/(1.4267 x 102) = 8.95773 3) 12.01 + 35.2 + 6 = 53.21 4) 55.46 28.9 = 26.56 5) 0.021 x 3.2 x 100.1 = 6.72672 6) 0.15 + 1.15 + 2.051 = 3.351 7) 150 / 4 = 37.5 8) 505 450.25 = 54.75
Express the sum of 7.68 m + 5.0 m using the correct number of significant digits. A.) 12.68 m B.) 12.7 m C.) 13 m D.) 10 m
Express the product of 2.2 mm x 5.00 mm using the correct number of significant digits. A.) 10 mm B.) 11 mm C.) 11.0 mm D.) 11.00 mm
Express 1111 km + 222 km using the correct number of significant digits. A.) 1300 km B.) 1330 km C.) 1333 km D.) 1333.0 km
Accuracy & Precision Accuracy how well measured value agrees with accepted value (correct) Precision how well measurement can be reproduced (reproducible using 2+ measurements)
Accuracy & Precision
Three different people weigh a standard mass of 2.00 g on the same balance. Each person obtains a reading of 7.32 g for the mass of the standard. These results imply that the balance that was used is. A.) accurate B.) precise C.) accurate and precise D.) neither accurate nor precise
Accepted Mass = 47.42 grams Lissa Inaccurate and Imprecise Lamont Accurate and Precise Leigh Inaccurate but precise Lissa Lamont Leigh 1 47.13 47.45 47.95 2 47.94 47.39 47.91 3 46.83 47.42 47.89 4 47.47 47.41 47.93
Determining Error Error difference between experimental value and accepted value Accepted value correct or known value Experimental value value measured in lab
Percent Error Percent Error a numeric way of expressing how accurate a value is in respect to the accepted value Percent Error = experimental value accepted value accepted value x 100
Percent Error Example Experimental value: 99.1 C Accepted value: 100 C What is the percent error?
Percent Error Example
Do This Now! 6 / 1 =? 3 / 3 =? 5 x 1 =?
Unit Conversions: Factor Label Method 1) Write the value you are given with units 2) Make it a fraction by placing it over 1
Unit Conversions: Factor Label Method 3) Multiply it by an equivalent fraction Units you want to cancel on bottom Units you want on top Fill in values so that they are equivalent * Metric: Place a one in front of the larger unit and how every many times smaller the other value is in front of it
Unit Conversions: Factor Label Method 4) Cross out units that are on both top and bottom 5) Perform math multiply across top, multiply across bottom, and then divide 6) Make sure you final answer has units and makes sense Should it have gotten bigger or smaller?
Practice 1. 55 L = ml 2. 22.3 cm = m 3. 3.2 kg = g 4. 354 mg = g 5. 7800 cm = km 6. 0.0085 mg = kg 7. 945 m/s = km/ min
Unit 1 Test Make Readings Using Measurement Rule Determine Number of Sig Figs in a Value Operations Using Sig Figs Unit Conversions Using Factor Label Method Must Know Metric Prefixes Scientific Notation Expanded Form Apply Terms Accuracy & Precision to Lab Data Percent Error Calculations Lab Apparatus Names Uses (Matching)