2 Scientific notation expresses numbers as a multiple of two factors: a number between 1 and10; and ten raised to a power, or exponent. 6.02 X 10 23 Scientific Notation
3 When numbers larger than 1 are expressed in scientific notation, the power of ten is positive. 2500 = 2.5 X 10 3 When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative..0025 = 2.5 X 10 -3
4 Change the following data into scientific notation. A. The diameter of the Sun is 1 392 000 km. C onvert Data into Scientific Notation B. The density of the Sun’s lower atmosphere is 0.000 000 028 g/cm 3.
5 Convert Data into Scientific Notation Move the decimal point to produce a factor between 1 and 10. Count the number of places the decimal point moved and the direction.
6 Remove the extra zeros at the end or beginning of the factor. Convert Data into Scientific Notation Remember to add units to the answers.
Measuring The numbers are only half of a measurement. It is 3 long. 3 what. Numbers without units are meaningless. How many feet in a yard? 3 ft You always need a numerical and unit value!
9 In 1795, French scientists adopted a system of standard units called the metric system. In 1960, an international committee of scientists met to update the metric system. The revised system is called the Système Internationale d’Unités, which is abbreviated SI.
10 Units of Measurement Throughout any natural science course we are going to deal with numbers. Numbers by themselves are meaningless. That is why need to have some sort of reference or standard to compare to. International System of Units or SI units, is based on the metric system. Quantity Base Unit Symbol LengthMeterm Mass Gram (Kilogram) g (kg) TimeSeconds TemperatureKelvink Amount of substance Molemol Electric current ampereA
11 Prefixes of the SI Units Since the SI Units are based upon the metric system, we use prefixes to change the quantity we are discussing about which use multiples of ten. Some standard prefixes are: PrefixAbbreviationMeaning Mega-M 10 6 Kilo-k 10 3 Deci-d 10 -1 Centi-c 10 -2 Milli-m 10 -3 Micro-µ 10 -6 Nano-n 10 -9 Pico-p 10 -12 Examples: 1 megabyte = 1,000,000 bytes 1 microgram = 0.000001 grams
Converting how far you have to move on a chart, tells you how far, and which direction to move the decimal place. You need the base unit : (meters, Liters, grams,) etc. You need a chart! You need a plan!
Dr – uL Rule 21.5 g = __________mg 345.6 m = ___________ km 21,500 0.3456 D own r ight u p L eft Giga1 000 000 000G 10 9 Mega1 000 000M 10 6 kilo1 000k1000 = 10 3 hecto1 00h100 = 10 2 deka10da10 = 10 1 BASE1g, L, sec, m, etc. 1 = 10 0 deci1/10d.1 = 10 -1 centi1/100c.01 = 10 -2 milli1/1 000m.001 = 10 -3 micro 1/1 000 000μ 10 -6 nano 1/1 000 000 000n 10 -9 pico 1/1 000 000 000 000p 10 -12
Conversions Change 5.6 m to millimeters khDdcm l starts at the base unit and move three to the right. l move the decimal point three to the right 5600
Conversions convert 25 mg to grams convert 0.45 km to mm convert 35 mL to liters It works because the math works, we are dividing or multiplying by 10 the correct number of times khDdcm
21 Accuracy and Precision When scientists make measurements, they evaluate both the accuracy and the precision of the measurements. Accuracy refers to how close a measured value is to an accepted value. Precision refers to how close a series of measurements are to one another.
22 Accuracy and Precision Precision –A measurement of how well several determinations of the quantity agree. Accuracy –The agreement of a measurement with the accepted value of the quantity.
23 Accuracy and Precision An archery target illustrates the difference between accuracy and precision.
Significant Figures Let’s take a look at some instruments used to measure --Remember: the instrument limits how good your measurement is!!
Uncertainty in Measurements Different measuring devices have different uses and different degrees of accuracy.
Significant figures (sig figs) We can only MEASURE at the lines on the measuring instrument We can (and do) always estimate between the smallest marks. 21345 in
4.5 inches What was actually measured? What was estimated? 4 inches 0.5 inches 21345 in
Significant figures (sig figs) The better marks… the better we can measure. Also, the closer we can estimate 21345 inin 21345 inin
21345 4.55 inches What was actually measured? What was estimated? inin 4.5 inches 0.05 inches
So what does this all mean to you? Whenever you make a measurement, you should be doing three things…… 1.Check to see what the smallest lines (increments) on the instrument represent 2.Measure as much as you can (to the smallest increment allowed by the device) 3.Estimate one decimal place further than you measured
Decimal Places Review 23456.789 thousandths hundredths tenths ones tens hundreds thousands ten thousands Your estimate MUST always be one (and only one) decimal place further to the right than your measurement
Practice Your graduated cylinder can only accurately measure to tens of mL. To what decimal place should you estimate? A balance can accurately measure to hundredths of grams. What decimal place will your estimate be?
Work Backwards Now L ook at the following measurements and determine the smallest increment that the measuring instrument could accurately measure to. Keep in mind that the last significant figure is the estimate. 100.3 g 207 L 1500 cm 0.0004467 kg ones tens thousands One-hundred thousandths
What is measured and what is estimated in the following measurements? ( Remember, significant figures include measured & estimated digits ) 100.3 207 1500 0.0004467 4 Sig Figs ; Measured: 100. ; Estimated: 0.3 3 Sig Figs ; Measured: 2.0 X 10 2 ; Estimated: 7 2 Sig Figs ; Measured: 1000 ; Estimated: 500 4 Sig Figs ; Measured: 0.000446; Est: 0.0000007
Significant Figures The term significant figures refers to digits that were measured. When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.
Significant Figures 1.All nonzero digits are significant. 2.Zeroes between two significant figures are themselves significant. 3.Zeroes at the beginning of a number are never significant. 4.Zeroes at the end of a number are significant if a decimal point is written in the number.
Significant Figures What about the Zeros?? BME NAP B Beginning M Middle E End N Never A Always P Point
Significant Figures in Calculations When addition or subtraction is performed, answers are rounded to the least significant decimal place. When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.
Sig figs. How many sig figs in the following measurements? 458 g 4085 g 4850 g 0.0485 g 0.004085 g 40.004085 g
Sig. Fig. Calculations Multiplication/Division Rules: The measurement w/ the smallest # of sig. figs determines the # of sig. figs in answer Let’s Practice!!! 6.221cm x 5.2cm = 32.3492 cm 2 4 2 How many sig figs in final answer??? And the answer is…. 32 cm 2
For example 27.936.4 =+ l First line up the decimal places + Then do the adding 34.33 Find the estimated numbers in the problem 27.93 6.4 This answer must be rounded to the tenths place = 34.3
Practice 4.8 + 6.8765= 520 + 94.98= 0.0045 + 2.113= 6.0 x 10 2 - 3.8 x 10 3 = 5.4 - 3.28= 6.7 -.542= 500 -126= 6.0 x 10 -2 - 3.8 x 10 -3=
9/19/201546 Dimensional Analysis The “Factor-Label” Method –Units, or “labels” are canceled, or “factored” out
9/19/201547 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.
9/19/201548 Dimensional Analysis Lining up conversion factors: 1 in = 2.54 cm 2.54 cm 1 in = 2.54 cm 1 in 1 in = 1 1 =
9/19/201549 Dimensional Analysis How many milliliters are in 1.00 quart of milk? 1.00 qt 1 L 1.057 qt = 946 mL qtmL 1000 mL 1 L
9/19/201550 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. lbcm 3 1.5 lb 1 kg 2.2 lb = 35 cm 3 1000 g 1 kg 1 cm 3 19.3 g
9/19/201551 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 in 3 L 1 L 1000 cm 3
9/19/201552 Dimensional Analysis 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 cmin
9/19/201553 Dimensional Analysis Taft football needs 550 cm for a 1st down. How many yards is this? 550 cm 1 in 2.54 cm = 6.0 yd cmyd 1 ft 12 in 1 yd 3 ft
9/19/201554 Dimensional Analysis 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 cmpieces 1 piece 1.5 cm
9/19/201555 Density is a ratio that compares the mass of an object to its volume. Density The units for density are often grams per cubic centimeter (g/cm 3 or g/mL). You can calculate density using this equation:
9/19/201556 If a sample of aluminum has a mass of 13.5 g and a volume of 5.0 cm 3, what is its density? Density Insert the known quantities for mass and volume into the density equation. Density is a property that can be used to identify an unknown sample of matter. Every sample of pure aluminum has the same density.
9/19/201557 % Error % error = O - A X 100 A O = experimental value obtained (observed) A = actual value (what you should get: text book)
9/19/201558 % Error 1.) What is the percent error in a lab if you find the reaction produces12.052 grams of calcium oxide. The text shows this reaction should produce 13.512 grams.