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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 = 2). 14 hL = L 3). 245 kilograms= 4). 0.083 mm= mm mg 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 Subtracting Be 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 Complete the following addition and subtraction problems 0.0045834 mm 438,904 s 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 The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out g cm g 3 cm 3 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 = 556.75g 5.5675 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)
