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Transcript of Measurement
Why would ALL scientists (yes even those in Fantasia) use the same units for their measurements? When we use the Metric System there are 7 base units. lets measure the length of a red blood cell http://learn.genetics.utah.edu/content/begin/cells/scale/ That red blood cell is .00008 m
that is pretty small can we rewrite that number so we don't have to write all those zero's? That number can be written as 8 micrometers Is there an easy way to remember the prefixes? We use Prefixes to do this All measurements contains some sort of error. No instrument is perfect nor is the person reading the instrument. Precision & Accuracy The derived unit of
DENSITY how 'compact' an object is mass: the amount of matter in an object
volume: the amount of space an object occupies whats density? Density = mass volume what are the units? (g) (ml) or (cm^3) so how do we calculate density? find the mass... find the volume... (volume displacement or direct measure)
divide the two BIG question...
can the density of an object change? NO. If the object stays the same, it has the same density EXPERIMENT!!! Scientists worry about their measurements in two ways How close is the measured value to the "true" or target value? Accuracy How repeatable are the measurements? How close are they to each other? Precision how would you describe this picture? poor accuracy & poor precision What would you say about this picture? high precision but low accuracy How about this one? high precision and high accuracy Is it possible to have high accuracy but low precision? Uncertainty in measurements we know they are not always perfect... precision and accuracy is always limited by the scale of the instrument (our lab!!!)
the more finely divided the scale, the more precise and accurate the measurement Look at the volume in this graduated cylinder make an estimate of the volume: remember the "guess" factor? 6.61ml "certain"digits: can be read right from the scale "Uncertain" digit: must be read between the lines Rule of thumb: when reporting measurements, record all certain digits plus the first uncertain digit. The numbers recorded in a measurement are called significant figures Estimate the length of this block (in cm) with the correct number of significant figures 2.24cm remember to guess the last number... Its going to be one number "BETWEEN THE LINES" you never have to question "where do I round" Significant Figures While taking measurements we need to be mindful of significant figures. Especially when we use measurements in various calculations. What is the uncertainty in our measurements and in our calculated value? Why would knowing the uncertainty be useful? How about an example? What is the density of the rock of granite shown below if its mass is 156.7 grams and its volume is 58.7cm^3? D=m/v D= 156.7g/58.7cm^3 = 2.6695060g/cm^3 hold up... can we really be sure of this answer out to 7 decimal places? it matters that we have accurate reports We have very precise measuring tools this day and age. However as a scientists we cannot claim greater precision than our instruments allow us. Lets ask Michael Phelps! we should never report more sig figs in a calculated value than were in the basic measurements to begin with Rules for counting Significant Figures If it isn't a zero, IT IS SIGNIFICANT! you must count it: 23.4 has 3 significant figures
2784 has 4 significant figures
How many does 1.56 have? ZERO'S ARE WIERD and their are 3 "kinds" of zeros: 1. leading zeros: NEVER COUNT 000357 3 sig figs
0.0063 2 sig figs
How about 0.023? 2. sandwiched zeros: ALWAYS COUNT 6.036 4 sig figs
56004 5 sig figs
How about 0.804? 3. trailing zeros: COUNT ONLY IF THERE IS A DECIMAL 6.200 4 sig figs
6700 2 sig figs
How about 0.4090? Ready... Set... Sig Fig!!! How many significant figures are in the following numbers? 340 0.0340 609.840
9080 1.0060 0.3056 Significant Figures in Calculated values 1. For multiplication and division: the LEAST number of SIGNIFICANT FIGURES in the problem is the number you can have in your answer. EX: 23.123123 (8 sig figs)
X 1.3344 (5 sig figs)
= 30.855495 (on calculator)
round to 30.855 (rounded to 5 sig figs the LEAST number) 2. For addition and subtraction: the LEAST number of DECIMAL PLACES in the problem is the number you can have in the answer. 23.112233 (6 places after decimal point)
+ 1.3324 (4 places after decimal point)
+ 0.25 (2 places after decimal point)
= 24.694633 (on calculator)
24.69 (rounded to 2 places the least number decimal places) EX: While experimenting to determine the density of an unknown gas, it is found that 1.82L of the gas has a mass of 5.430g. What is its density in g/L rounded to correct sig figs? A room measures 11.5m x 8.00m. What is the perimeter of the room, rounded to the correct number of significant figures? why do we use this anyway? Scientific Notation A number in Scientific Notation:
shows the precision of our measurements because it allows the correct number of significant figures to be expressed A measurement of 50cm can show an unclear number of significant figures remember our rules... how many sig figs does 50 cm have? We can write 50cm as:
5 x 10^1 (1 sig fig)
5.0 x 10^2 (2 sig figs) Or you can think about it like this... Scientific Notation also allows you to reduce the number of zeros written 3.32 X 10^5 number between 1 and 10 base of 10 raised to some exponent Switching into and out of Scientific Notation 4.8 X 10^7 If the exponent is positive --> your decimal moves to the right. 4.8 X 10^-7 If the exponent is negative --> your decimal moves to the left 67,400,000 find your decimal and move it to make a number between 1 & 10
If you move the decimal left --> your exponent will be positive .000000467 find your decimal and move it to make a number between 1 & 10
If your decimal moves right --> you exponent will be negative Do you notice the number and exponent go in opposite directions? 1. Addition & Subtraction When adding two numbers in scientific notation, their exponents must be the same. The two numbers are added while the exponent stays the same ex. 4.2 X 10^4 + 7.9 X 10^3 One must be changed to look like the other... 4.2 X 10^4
+0.79 X 10^4 = 4.99 X 10^4 2. Multiplication When multiplying two numbers in scientific notation, the exponents are added. The two integers are multiplied while the exponents are added ex. (5.23 X 10^6) (7.1 X 10^-2) = 37.133 X 10^4 adjust to correct notation and two significant figures = 3.7 X 10^5 3. Division When dividing two numbers in scientific notation, you subtract the exponents. The integers are divided and the exponents are subtracted ex. 5.44 X 10^7
8.1 X 10^4 = 0.671604 X 10^3 adjust to correct notation and two significant figures = 6.7 X 10^2