unit ii.5 significant figures. ii.5 significant figures measuring vs. counting: imagine we are...
TRANSCRIPT
UNIT II.5Significant Figures
II.5 SIGNIFICANT FIGURES
Measuring vs. Counting: Imagine we are picking apples and we count
the apples as we go. We can count exactly how many we pick (ex: 30 apples). If we wanted to measure the mass of the apples, it could be done but we cannot measure the EXACT mass of the apples.
There is always some ___________________ associated with measurements.
II.5 SIGNIFICANT FIGURES
There are 2 things we need to learn:1.
2.
II.5 SIGNIFICANT FIGURES
1. SIGNIFICANT FIGURES A. Definition A significant figure (sig fig) is
Ex:
II.5 SIGNIFICANT FIGURES
All non-zero digits are significant.
Ex.
All zero digits between non-zero digits are significant.
Ex.
II.5 SIGNIFICANT FIGURES
Leading zeroes are NOT SIGNIFICANT.
Ex:
II.5 SIGNIFICANT FIGURES
Trailing zeroes are ONLY SIGNIFICANT WHEN A DECIMAL POINT IS PRESENT.
Ex:
QUESTION: p. 37 #55
II.5 SIGNIFICANT FIGURES
B. Accuracy and Precision
An ACCURATE measurement =
A PRECISE measurement =
II.5 SIGNIFICANT FIGURES
*Note: we calibrate instruments (especially balances) to ensure accuracy. Calibration involves measuring the mass of a known object and adjusting the balance until we obtain the desired reading. The balance has then been “calibrated”!
Example: P 29 #43
II.5 SIGNIFICANT FIGURES
Assume you have a balance which gives very precise measurements. What might be true about the balance that its readings would be precise but not accurate?
QUESTIONS: p. 29 #44, 45
II.5 SIGNIFICANT FIGURES
C. Measuring an object or substance…. The NUMBER of significant figures =
Examples:
* If you are given a measurement without any additional info, assume that the LAST DIGIT is _______________________.
Ex: 45. 7
II.5 SIGNIFICANT FIGURES
D. Defined Numbers and Counting Numbers
Examples:
QUESTIONS: p. 29 #46, 47
II.5 SIGNIFICANT FIGURES
2. HOW TO READ A SCALE Terms:
II.5 SIGNFICANT FIGURES
Example (a) on p. 30:
1st 2 digits are 6.2 1st 2 digits are 6.3
II.5 SIGNIFICANT FIGURES
#1: Find the DIFFERENCE between each numbered division:
#2: Find the value of the unnumbered division: *Value at (i) *Value at (ii)
#3: Estimate the uncertain digit:
*Value at (i) *Value at (ii)
II.5 SIGNIFICANT FIGURES
*NOTE: if the pointer appears to be exactly on one of the marking:
Example:
QUESTION: p. 32 #48
II.5 SIGNIFICANT FIGURES
3. EXPERIMENTAL UNCERTAINTY Definition:
Experimental uncertainty =
II.5 SIGNIFICANT FIGURES
Ex: 39.1 0.1 C Means that the actual value lies in the range
of
*The measurement reported is the _______________________ of the range (midpoint is the average of the endpoints).
II.5 SIGNIFICANT FIGURES
4. MULTIPLYING & DIVIDING NUMBERS
Ex:
II.5 SIGNIFICANT FIGURES
Notes *Sometimes you will have to put your
number in scientific notation to have the correct # of sig figs:
Ex:
II.5 SIGNIFICANT FIGURES **Exponential parts of the number do NOT
contribute to the # of sig figs:
Ex: 3.2 x 103
*** When performing calculations, don’t ROUND until the end (final answer).
QUESTION: p. 39 #56 (odd)
II.5 SIGNIFICANT FIGURES
4. ADDING & SUBTRACTING NUMBERS Ex: 11.467 cm
+ 12.31 cm *Adding numbers in scientific notation: Ex:
II.5 SIGNIFICANT FIGURES **Reminder:
QUESTIONS: p. 40 #57 and 58 (odd)
ASSIGNMENT