units and standards. in science, numbers aren’t just numbers. they need a unit. we use standards...
TRANSCRIPT
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Units and Standards
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Units and Standards
• 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
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Units and Standards
• 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.
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Units and Standards
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Units and Standards
• Conversions in the SI are easy because everything is based on powers of 10
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Units and Standards
• Ex. Length.• Base unit is meter.
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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
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Scientific Notation
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Scientific Notation
A short-hand way of writinglarge numbers without writing all of the zeros.
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Scientific notation consists of two parts:
A number between 1 and 10
A power of 10
N x 10x
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The Distance From the Sun to the Earth
149,000,000km
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Step 1
Move the decimal to the left
Leave only one number in front of decimal
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Step 2
Write the number without zeros
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Step 3
Count how many places you moved decimal
Make that your power of ten
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The power often is 7 becausethe decimalmoved 7 places.
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93,000,000 --- Standard Form
9.3 x 107 --- Scientific Notation
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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
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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
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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
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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
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Practice:Write in Standard Form
6.27 x 106
9.01 x 104
6,270,000
90,100
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Accuracy, Precision and Significant Figures
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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?
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Accuracy & Precision
Precision: How closely two or more measurements
of the same quantity agree with one another.
Think: Can the measurement be consistently reproduced?
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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
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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
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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 ________
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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
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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
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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
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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
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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
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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