1 using numbers in science metric system and instruments used for measurement
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Using Numbers in Science
Metric System and Instruments Used for Measurement
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Parts of a Measurement
1. The value (numerical portion)
2. The unit (describes what units)
3. The name of substance being measured
EX:
1 teaspoon salt
2 liters of pop
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Scientific Measurements
• Made in metric units• Referred to as the International System or
SI units• Based on the decimal system• Related by powers of 10• Each type has a base unit• Use prefixes to refer to a unit larger or
smaller than the base by some power of 10
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kilo hecto deca Base Unit
deci centi milli micro
k h da gram (g) d c mm μ
1000 100 10 liter (L) .1 .01 .001 0.000001
103 102 101 meter (m) 10-1 10-2 10-3 10-4 10-5 10-6
Metric Unit Conversions
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Kilometer
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Meter
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Centimeter
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Review of Metric System
• Nano = 1/100,000,000 = 0.000000001 • Micro = 1/1,000,000 = 0.000001 • XXX• XXX• Milli = 1/1,000 = 0.001• Centi = 1/100 = 0.01• Deci = 1/10 = 0.1• BASE UNIT = 1• Deca = 10 = • Hecto = 100• Kilo = 1000
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Comparison Ideas
equals
equals
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SI (International System) unitsLength meter m
Mass kilogram kg
Temperature Kelvin K
Time second S
Volume Liter L
Centigrade or Celsius = ºC This is the unit we will use in lab for temperatures!
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Uncertainty in Measurement
• No matter how careful you are
• No matter how carefully you read the measuring instrument
• No measurement is perfectly accurate
• The quality of our measurements are stated in terms of accuracy and precision
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Measured numbers
-are an estimated amount
-measured to a certain number of significant figures
-a numerical value with attached units that expresses a physical quantity such as length, mass, volume, time or temperature.
Uncertainty in Measurement
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•Error: is the difference between the true value and our estimate, or measurement, of the value.
•Accuracy: is the degree of agreement between the true value and the measured value.
•Precision: is a measure of the agreement of replicate measurements
•Uncertainty: is the degree of doubt in a single measurement.
Uncertainty in Measurements
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Accuracy
= of a measurement is how close that measurement is to the true or “exact” value
EX: Standard weight = 5.00g
4.98g more accurate than 5.12 g
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Accuracy
• Also subject to the reliability of the measuring instrument
• The smaller the increments of units on the instrument, the more accurate
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Length Measurements
• Ruler A has more uncertainty and gives less precise measurements.
• Ruler B has less uncertainty and gives more precise measurements.
Measuring the length of a metal rod
Metric Rulers for Measuring Length.
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Precision
• Precision = making reproducible or repetitive measurements of the same quantity
• How fine the divisions are
• There will always be some uncertainty because of the limits in the accuracy of your instruments
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It is also possible to have an accurate
measurement without being
precise.
Imprecise andinaccurate
Precise andaccurate
Precise butinaccurate
Precision versus Accuracy
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“Accuracy is telling the truth…..
Precision is telling the same story over and over again.”
Yiding Wang
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• Strive for measurements that are accurate and precise
• Measurements you perform will be used in subsequent calculations
• In scientific measurements all the digits known w/certainty, plus the one estimated digit, are known as significant figures or significant digits.
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Significant figures: is defined to be all digits in a number representing data or results that are known with certainty plus the first uncertain digit.
0 1 2 3 4 5 6 7 8 9 10 cm
5.48 cm
0 1 2 3 4 5 6 7 8 9 10 cm
5.4 cm
Significant Figures
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Significant figures or Significant digits
• ANY numbers generated by means of a measurement (length, volume, time, etc) should be expressed in the correct number of significant figures.
• This reflects how close the measured values are to the true values.
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Significant Figures (digits)= reliable figures obtained by
measurement= all digits known with certainty plus
one estimated digit
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Taking the measurement
• Is always some uncertainty
• Because of the limits of the instrument you are using
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EXAMPLE: mm ruler
Is the length of the line between 4 and 5 cm? Yes, definitely.Is the length between 4.0 and 4.5 cm? Yes, it looks that way. But is the length 4.3 cm? Is it 4.4 cm?
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• It is important to be honest when reporting a measurement, so that it does not appear to be more accurate than the equipment used to make the measurement allows.
• We can achieve this by controlling the number of digits, or significant figures, used to report the measurement.
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As we improve the sensitivity of the equipment used to make a measurement,
the number of significant figures increases. Postage Scale
3 g
1 g 1 significant figure
Two-pan balance
2.53 g
0.01 g 3 significant figures
Analytical balance
2.531 g
0.001g 4 significant figures
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Which numbers are Significant?
How to count them!
55.00 mm
0.003g
9000 L
5,551,213
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Non-Zero integers
• Always count as significant figures
1235 has 4 significant digits
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Zeros – there are 3 types
Leading zeros (place holders)
The first significant figure in a measurement is the first digit other than zero counting from left to right
0.0045g
(4 is the 1st sig. fig.)
“0.00” are place holders.
The zeros are not significant
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Captive zeros
Zeros within a number at always significant – 30.0809 g
All digits are significant
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Trailing zeros – at the end of numbers but to the right of the decimal point
2.00 g - has 3 sig. digits (what this means is that the measuring instrument can measure exactly to two decimal places.
100 m has 1 sig. digit
Zeros are significant if a number contains decimals
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Exact Numbers
Are numbers that are not obtained by measuring
Referred to as counting numbers
EX : 12 apples, 100 people
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Exact Numbers
Also arise by definition
1” = 2.54 cm or 12 in. = 1 foot
Are referred to as conversion factors that allow for the expression of a value using two different units
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Rules for sig figs.:•Count the number of digits in a measurement from left to right:
•Start with the first nonzero digit•Do not count place-holder zeros.
•The rules for significant digits apply only to measurements and not to exact numbers
Sig figs is short for significant figures.
Significant Figures
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Determining Significant Figures
State the number of significant figures in the following measurements:
2005 cm
25,000 g
25.0 ml
0.25 s
0.00250 mol
4
2
3
2
3
0.050 cm
0.0280 g
50.00 ml
1000 s
1000. mol
2
3
4
1
4
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Rounding Numbers
• To express answer in correctly
• Only use the first number to the right of the last significant digit
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Rounding
• Always carry the extra digits through to the final result
• Then round
EX:
Answer is 1.331 rounds to 1.3
OR
1.356 rounds to 1.4
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Rounding off sig figs (significant figures):
Rule 1: If the first non-sig fig is less than 5, drop all non-sig fig.Rule 2: If the first sig fig is 5, or greater that 5, increase the last sig fig by 1 and drop all non-sig figs.
Round off each of the following to 3 significant figures:
12.514748 12.5 0.6015261 0.602
192.49032 192 14652.832 14,700
Significant Figures
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Measurements With a Ruler orMeter Stick – Look at it FIRST! –
Where is “0”
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Protractor for Measuring Angles
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Measuring Angles Units are degrees (º)
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Practice Time
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Using a Vernier Caliperhttp://phoenix.phys.clemson.edu/labs/cupol/vernier/
•Used to accurately determine the fraction part of the least count division.
•Length of an object, the outer diameter (OD) of a round or cylindrical object, the inner diameter (ID) of a pipe, and the depth of a hole.
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Parts of a Caliper
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• The caliper consists of a main scale engraved on a fixed ruler and an auxiliary caliper scale engraved on a movable jaw
• The movable auxiliary scale is free to slide along the length of the fixed ruler.
• The main scale is calibrated in centimeters with the smallest division in millimeters.
• The auxiliary scale has 10 divisions that cover the same distance as 9 divisions on the main scale. Therefore, the length of the auxiliary scale is 9.0 mm.
Auxillary (Venier) Scale
Main scale
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• When the caliper is closed and properly zeroed the first mark (zero) on the main scale is aligned with the first mark on the auxiliary scale.
• The last mark on the auxiliary scale will then coincide with the 9 mm-mark on the main scale.
• This is read 0.00 cm.
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• Once the caliper is positioned to make a reading, make a note of where the first mark on the auxiliary scale falls on the main scale.
• We see that the object's length is between 1.2 cm and 1.3 cm because the first auxiliary mark is between these two values on the main scale.
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• The last digit (tenths of a millimeter) is found by noting which line on the auxiliary scale coincides with a mark on the main scale.
• The last digit is 3 because the third auxiliary mark lines up with a mark on the main scale. T
• The length of the object is 1.23 cm.
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Practice Time!
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