Transcript measurements - New York Science Teacher

MEASUREMENTS
Kenneth E. Schnobrich
WHAT DO WE HAVE TO DO?
1. WE MUST DEFINE WHAT IT IS WE ARE GOING
TO MEASURE
2. WE MUST ESTABLISH A STANDARD
3. WE MUST DEVELOP SOMETHING TO COMPARE
TO THE STANDARD
NORMAL MEASUREMENTS
1. LENGTH
2. MASS
3. TIME
4. TEMPERATURE
TYPICAL UNITS
UNIT
DEFINITION
STD
COMPARE
LENGTH
Dist. Between
2 points
Meter
Metric rule
MASS
Quantity of
matter
grams or
kilograms
Balance
TIME
Interval
between 2
events
Second
Timer/clock
TEMP.
Measure of
avg. K.E.
°C or K
thermometer
BASIC vs DERIVED
Basic Units or Fundamental Units are those we just
mentioned
1. Length
2. Mass
3. Time
4. Temperature
BASIC vs DERIVED
Derived Units are combinations of the basic units
1. Area
LxW
2. Volume
LxWxH
3. Density
Mass/Volume
4. Energy
Joule (kg•m2/s2) or calorie
5. Pressure
Pa = kg/m•s2
WHY THE METRIC SYSTEM?
• BASED ON DIVISIONS OF OR MULTIPLES
OF TEN
• THERE ARE COMMON PREFIXES
• THE SYSTEM IS WIDELY ACCEPTED
COMMON PREFIXES
Prefix
Mega
Kilo
Hecto
Deca
Deci
Centi
Milli
Micro
Nano
Symbol
M
k
h
D
d
c
m
µ
n
Meaning Exp. Not.
1,000,000.
106
1,000.
103
100.
102
10.
101
0.1
10-1
0.01
10-2
0.001
10-3
0.000001
10-6
0.00000001
10-9
UNIT CONVERSIONS
Convert 25.4 kg to g:
25.4 kg
x (1000 g/kg) =
25400 g
Convert 8500 m to mm:
8500 m
x
(1000 mm/m) = 8500000 mm
WHAT IS A SIGNIFICANT
FIGURE?
When you are making a measurement there are
always a certain number of known or certain digits.
Then as part of the measurement there will always
be a digit that is uncertain because it is your guess.
The known or certain digits plus the first unknown
Digit are referred to as the SIGNIFICANT FIGURES
PRECISION vs ACCURACY
PRECISION: this refers to a situation where the same
result is gotten each time you perform the operation
• repeatedly hitting the same spot in darts
ACCURACY: this refers to how close you come to
the accepted value or result
• how close you are to the bullseye
SIGNIFICANT FIGURES
The following rules apply to significant figures:
1. All digits in a measurement are considered significant
2. Zeros that fall between digits are considered
significant
3. Zeros to the right of a decimal and to the left of a
non-zero are considered significant
4. If a decimal point is placed after a zero all of the
intervening zeros are significant
5. Zeros after a digit but not followed by a decimal are
not significant
EXACT NUMBERS
These are usually numbers that are obtained by
counting rather than using a measuring device
such as a buret or graduated cylinder - 12 eggs in a
dozen, 2 socks in a pair, 144 things in a gross
SIGNIFICANT FIGURES
Working with Significant figures:
1. When you add or subtract numbers:
the final answer can have no more decimal
places than the least precise value in the operation
2. When you multiply or divide numbers:
the final answer can have no more significant
figures than the smallest number of significant
figures in the operation
EXAMPLES
ADDING & SUBTRACTING:
5.0043
5.0043
4.032
1.02
1.02
4.02
3.2
13.3
EXAMPLES
Multiplying and Dividing
4.91
5.0043
4.032
20.33
1.02
5.0043
MORE EXAMPLES
How many Significant figures in each of the following:
1. 0.0043
2. 1.0043
3. 14300
4. 5820.
5. 30089
6. 2.0607
MORE EXAMPLES
How many Significant figures in each of the following:
1. 243.0 x 1.8 =
2. 1.0043 + 2.08 =
3. 14300/4 =
4. 5820. x 4.32 =
5. 30089 - 7.32 =
6. 2.0607 + 3.85 =
ROUNDING
When rounding use only the first digit to the right of the last
significant figure . 4.348 becomes 4.3 if rounded to 2 sig.figs.
Rules:
-In a series of calculations, carry the extra digits through to
the final result, then round.
-If the digit to be removed
-Is less than 5 the preceding digit stays the same. 1.33
becomes 1.3
-Is equal to or greater than 5, the preceding digit is
increased by 1. 1.36 becomes 1.4