1.2 Measurements and Uncertainties
description
Transcript of 1.2 Measurements and Uncertainties
![Page 1: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/1.jpg)
1.2 Measurements and Uncertainties
![Page 2: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/2.jpg)
1.2.1 State the fundamental units in the SI system
• In science, numbers aren’t just numbers. • They need a unit. We use standards for
this unit.• A standard is:
• a basis for comparison• a reference point against which other things
can be evaluated
• Ex. Meter, second, degree
![Page 3: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/3.jpg)
1.2.1 State the fundamental units in the SI system
• The unit of a #, tells us what standard to use.
• Two most common system:• English system• Metric system
• The science world agreed to use the International System (SI)• Based upon the metric system.
![Page 4: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/4.jpg)
1.2.1 State the fundamental units in the SI system
![Page 5: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/5.jpg)
1.2.1 State the fundamental units in the SI system
• Conversions in the SI are easy because everything is based on powers of 10
![Page 6: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/6.jpg)
Units and Standards
• Ex. Length.• Base unit is meter.
![Page 7: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/7.jpg)
Common conversions
2.54 cm = 1 in 4 qt = 1 gallon
5280 ft = 1 mile 4 cups = 48 tsp
2000 lb = 1 ton
1 kg = 2.205 lb
1 lb = 453.6 g
1 lb = 16 oz
1 L = 1.06 qt
![Page 8: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/8.jpg)
Scientific Notation
![Page 9: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/9.jpg)
1.2.2 Distinguish between fundamental and derived units and give examples of derived units.
Some derived units don’t have any special names
Quantity Name Quantity Symbol
Unit Name Unit Symbol
Area A Square meter
Volume V Cubic meter
Acceleration a Meters per second squared
Density p Kilogram per cubic meter
![Page 10: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/10.jpg)
1.2.2 Distinguish between fundamental and derived units and give examples of derived units.
Others have special names
Quantity Name Quantity Symbol
Special unit name Special unit Symbol
Frequency f Hz
Force F N
Energy/Work E, W J
Power P W
Electric Potential V V
![Page 11: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/11.jpg)
1.2.2 Distinguish between fundamental and derived units and give examples of derived units.
A derived unit is a unit which can be defined in terms of two or more fundamental units.
For example speed(m/s) is a unit which has been derived from the fundamental units for distance(m) and time(s)
![Page 12: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/12.jpg)
Scientific Notation
A short-hand way of writing large numbers without writing all of the zeros.
![Page 13: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/13.jpg)
Scientific notation consists of two parts:
A number between 1 and 10
A power of 10
N x 10x
![Page 14: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/14.jpg)
149,000,000km
![Page 15: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/15.jpg)
Step 1
Move the decimal to the left
Leave only one number in front of decimal
![Page 16: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/16.jpg)
Step 2
Write the number without zeros
![Page 17: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/17.jpg)
Step 3
Count how many places you moved decimal
Make that your power of ten
![Page 18: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/18.jpg)
The power often is 7 becausethe decimalmoved 7 places.
![Page 19: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/19.jpg)
93,000,000 --- Standard Form
9.3 x 107 --- Scientific Notation
![Page 20: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/20.jpg)
Practice Problem
1) 98,500,000 = 9.85 x 10?
2) 64,100,000,000 = 6.41 x 10?
3) 279,000,000 = 2.79 x 10?
4) 4,200,000 = 4.2 x 10?
Write in scientific notation. Decide the power of ten.
9.85 x 107
6.41 x 1010
2.79 x 108
4.2 x 106
![Page 21: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/21.jpg)
More Practice Problems
1) 734,000,000 = ______ x 108
2) 870,000,000,000 = ______x 1011
3) 90,000,000,000 = _____ x 1010
On these, decide where the decimal will be moved.
1) 7.34 x 108 2) 8.7 x 1011 3) 9 x 1010
![Page 22: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/22.jpg)
Complete Practice Problems
1) 50,000
2) 7,200,000
3) 802,000,000,000
Write in scientific notation.
1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011
![Page 23: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/23.jpg)
Scientific Notation to Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
340,000 in standard form
3.40000 --- move the decimal
![Page 24: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/24.jpg)
Practice:Write in Standard Form
6.27 x 106
9.01 x 104
6,270,000
90,100
![Page 25: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/25.jpg)
Accuracy, Precision and Significant Figures
![Page 26: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/26.jpg)
Accuracy & Precision
Accuracy: How close a measurement is to the true
value of the quantity that was measured.Think: How close to the real value is it?
![Page 27: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/27.jpg)
Accuracy & Precision
Precision: How closely two or more measurements
of the same quantity agree with one another.
Think: Can the measurement be consistently reproduced?
![Page 28: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/28.jpg)
Significant Figures
The numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include the known digits plus one estimated digit
![Page 29: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/29.jpg)
Three Basic Rules
Non-zero digits are always significant. 523.7 has ____ significant figures
Any zeros between two significant digits are significant. 23.07 has ____ significant figures
A final zero or trailing zeros if it has a decimal, ONLY, are significant. 3.200 has ____ significant figures 200 has ____ significant figures
![Page 30: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/30.jpg)
Practice
How many sig. fig’s do the following numbers have? 38.15 cm _________ 5.6 ft ____________ 2001 min ________ 50.8 mm _________ 25,000 in ________ 200. yr __________ 0.008 mm ________ 0.0156 oz ________
![Page 31: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/31.jpg)
Exact Numbers
Can be thought of as having an infinite number of significant figures
An exact number won’t limit the math.1. 12 items in a dozen 2. 12 inches in a foot 3. 60 seconds in a minute
![Page 32: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/32.jpg)
Adding and Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places.
25.2 one decimal place
+ 1.34 two decimal places
26.54 answer
26.5 one decimal place
![Page 33: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/33.jpg)
Practice:Adding and Subtracting
In each calculation, round the answer to the correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75 2) 256.8 3) 257
B. 58.925 - 18.2 =
1) 40.725 2) 40.73 3) 40.7
![Page 34: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/34.jpg)
Multiplying and Dividing
Round to so that you have the same number of significant figures as the measurement with the fewest significant figures.
42 two sig figs
x 10.8 three sig figs
453.6 answer
450 two sig figs
![Page 35: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/35.jpg)
Practice:Multiplying and
Dividing In each calculation, round the answer to the correct number of significant figures.
A. 2.19 X 4.2 =
1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 =
1) 61.58 2) 62 3) 60
![Page 36: 1.2 Measurements and Uncertainties](https://reader035.fdocuments.net/reader035/viewer/2022062217/56813c67550346895da5f4f5/html5/thumbnails/36.jpg)
Practice work
How many sig figs are in each number listed? A) 10.47020 D) 0.060 B) 1.4030 E) 90210 C) 1000 F) 0.03020
Calculate, giving the answer with the correct number of sig figs. 12.6 x 0.53 (12.6 x 0.53) – 4.59 (25.36 – 4.1) ÷ 2.317