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SI units: The International System of Units (abbreviated SI from the French Système international d'unités]) is the modern form of the metric system a system of units of measurement devised
around seven base units and the convenience of the number ten
1). Find your decimal point
2). Find your direction
3). Count your steps
4). Move the decimal
King Henry died by drinking chocolate milk
Example: 12 Kilograms = _____ Decigrams
Deci is 4 spaces to the left of Kilo so move the decimal 4 spaces to the right.
Answer: 12 kg = 120000 g
I will give you these conversion factors if you need them in a problem!
1 inch = 2.54 cm exactly 1 lb = 454 g 1 qt = 0.946 L 1 mi = 5280 ft 1 qt = 2 pt 4qt = 1 gal 1 ounce = 28.349523 grams
Convert 3598 grams into pounds.(exactly 1 lb = 454 g )
ANS: 7.925 lbs
Convert 231 grams into ounces.(1 ounce = 28.349523 grams)
ANS:8.15 ounces
How many gallons are in 5.67 L?(1 qt = 0.946 L and 4qt = 1 gal)
ANS: 1.50
Practice on your own 1). 5 decimeters = mm 2). 14 hL = L 3). 245 kilograms= mg 4). 0.083 mm= m
Scientific notation is simply a method for expressing, and working with, very large or very small numbers.
-Numbers in scientific notation are made up of three parts: the coefficient, the base and the exponent.
-EX: 5.67 x103 is the scientific notation for 5670
-5.67 x 103 coefficient base exponent
1. The coefficient must be greater than or equal to 1 and less than 10.
2. The base must be 10.
3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation. A negative exponent means that the decimal is moved to the left when changing to standard notation.
Move decimal until there’s 1 digit to its left.
-Places moved = exponent. Large # (>1) positive exponent Small # (<1) negative exponent EX: Put 987000000000000000 in
scientific notation
Practice
Adding and SubtractingBe sure that the exponents are the same
Then add or subtract the decimal number as listed
Multiplication and Division To multiply – multiply the first factors then add the exponents
To divide – divide the first factors then subtract the exponent of the divisor from the exponent of the dividend
Write the following numbers in scientific notation 0.0045834 mm 438,904 s
Complete the following addition and subtraction problems 6.23 x 106 kL + 5.34 x 107 kL 9.87 x 104 g – 6.2 x 103 g
Complete the following multiplication and division problems (4.8 x 105 km) x (2.0 x 103 km) (8.4 x 106 L) ÷ (2.0 x 103 L)
Dimensional Analysis A tool often used in science for converting units
within a measurement system Conversion Factor
A numerical factor by which a quantity expressed in one system of units may be converted to another system
3
3
cm
gcm
The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out
g
Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.
How many seconds are in 1.4 days?
Plan: days hr min seconds
1.4 days x 24 hr x 60 min x 60 sec = 1 day 1 hr 1 min
120960 sec
Calculate density and use density to identify pure substances Ratio of mass to volume Directly proportional measure of how tightly
matter is packed Substances can be identified by comparing
densities to known densities density (D) = mass (m) / volume (V)
Expressed in g/mL Density can be calculated by measuring the
change in volume by a specifically measured mass
A 5-mL sample of water has a mass of 5 g. What is the density of water?
An object with a mass of 10 g raises the level of water in a graduated cylinder from 25.1 mL to 30.1 mL. What is the density of the object?
The density of aluminum is 2.7 g/mL. What is the volume of 8.1 g?
EQ: In what ways do proper techniques contribute to reliable
results?
Distinguish between accuracy and precision in measurement Accuracy – extent to which a
measurement approaches the true value of a quantity Agreement of a measurement
with the accepted value of the quantity
Precision – degree of exactness or refinement of a measurement How close a series of
measurements are to one another.
France vs. Italy Italy converts all five penalty kicks to
win championship
2005 Yr:
Att= 453 Comp=305
%Pass Completion= 305/453 = 67.3 %
Calculating percent error % error = theoretical – actual x 100
theoretical
The accepted length of a steel pipe is 5-m. Calculate the percent error for each of these measurements 5.25 m 4.75 m 5.5 m
Rules recognizing significant figures Non-zero numbers are always significant Zeros between non-zero numbers are always
significant All final zeros to the right of the decimal place
are significant Zeros that act as placeholders are not
significant. Convert quantities to scientific notation to remove placeholder zeros
Counting numbers and defined constants have an infinite number of significant figures
Rounding Rules If the digit to the immediate right of the last
significant figure is less than five, do not change the last significant figure
If the digit to the immediate right of the last significant figure is greater than five, round up the last significant figure
If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure if odd. If even, do not round up.
How many significant figures in the following measurements? 431,801 kg 10,235.0 mg 0.004384010 cm 0.00986451cg
Write the above in scientific notation to four significant figures
Rules for using significant figures in calculations Addition or Subtraction
The answer can have no more digits to the right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point
10.03542 m+12.02 m
22.05542 m = 22.06 m = 2.21 X 101 m
Multiplication or Division The answer can have no more significant figures than there are in the measurement with the smallest number of significant digits
Problem:1.1135 g/mL x 500. mL = 556.75g5.5675 x 102g = 5.57 x 102g
Round the answers to each of the following problems to the correct significant figures 7.31 x 104 + 3.23 x 103
8.54 x 10-3 – 3.41 x 10-4
(2.4 x 102) x (3.26 x 104) (1.024 x 102) ÷ (5.12 x 101)
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