Measured & counted numbers When you use a measuring tool to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.
Counted numbers Obtained when you count objects 2 soccer balls 1 watch 4 pizzas Obtained from a defined relationship 1 foot = 12 inches 1 meters = 100 cm Not obtained with measuring tools
Measurements: Accurate or Precise? Creating definitions and clarifying terms
Precision Precision is the ability to _______________and come up with the same value every time. It is an indication of __________a series of measurements are to each other. In general, the more decimal places you have, the more precise your measurement is.
Precision The idea of precision is very closely aligned with the idea of significant figures. A large number of significant figures suggests a high degree of precision. In our next class we will learn all about sig figs. Now, relax
Which is the most precise balance?
Accuracy An indication of how ________________________ (often theoretical) The closer you are to the real, accepted value, the more accurate you are.
Accurate or Precise? Case 1 In the diagram, what can we say about the group of arrows in terms of accuracy: precision:
Accurate or Precise? Case 1 In the diagram, what can we say about the group of arrows in terms of accuracy: low (as a group) precision: low
Accurate or Precise? Case 2 In the diagram, what can we say about the group of arrows in terms of accuracy: precision:
Accurate or Precise? Case 2 In the diagram, what can we say about the group of arrows in terms of accuracy: low precision: high
Accurate or Precise? Case 3 In the diagram, what can we say about the group of arrows in terms of accuracy: precision:
Accurate or Precise? Case 3 In the diagram, what can we say about the group of arrows in terms of accuracy: high precision: high
Can we ever be 100% certain?? Nope! This is what we call ‘uncertainty’ in measurements.
Experimental uncertainty It is the estimated amount by which a measurement might be in error Usually expressed as +/- The smaller the uncertainty, the more the precision…
Experimental uncertainty Assume you measured a temperature to be 37.5 C° What would the uncertainty be? Uncertainty is always in the last digit! What does this mean?
Experimental uncertainty This means, the actual degree is somewhere between
How to read a measurement scale
Taking measurements
Example b) page 31
Volume readings
Graduated cylinder readings
Time to practice! Hebden page29 #44 page32 #48(A,C,E) page34 #50(A,D,G) page35 #51(A,C) and #52(A,B) I am here to help
Measurements Why do we care?????? Measured quantities have uncertainties in them. It is impossible to find the EXACT value…so what do we use?
Significant figures They are measured or meaningful digits. How do we know if a number is a ‘sig fig’ or not? Let us proceed, shall we?
Two major cases to know #1: When there are no decimal points #2: When there are decimal points
#1: when there are no decimal points Count every single number you see as a significant figure, EXCEPT for ZERO. BUT…..Zeroes in between two non-zero digits are significant. All other zeroes are insignificant.
#1: when there are no decimal points How many sig figs do the following numbers have?? 345, 5557, 300, 4120, 4005, 40050
#2: when there are decimal points Start from the left side of the number, ignore all the zero's on the left side of the decimal points ( aka leading zero's). Only start counting at the first non zero digit. Once you start counting, continue until you run out of digits.
#2: when there are decimal points Example: how many sig figs do the following numbers have? , , , 44.4,
Significant figures “sig figs” x do not expand
Significant figures “sig figs” x x
Adding and Subtraction with Significant Figures When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations
Adding and Subtraction with Significant Figures When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations
Adding and Subtraction with Significant Figures x x 10 4
Adding and Subtraction with Significant Figures x x 10 2
Adding and Subtraction with Significant Figures x x 10 -5
When changing exponents, remember…..if you change the lower exponent to the higher exponent. You are making the exponent larger so make the number smaller. It is a trade !
HOMEWORK PAGE 40 #57 (A,B,C,E,F,I,J)