Measurement All measurements should include a number and a unit. Measured quantities and (units) include: mass (kg); length (m); time (s); Newtons (force); energy (J)
Fundamental units can’t be broken down into more basic units. Include m, kg, s
Derived units can be broken down into more basic units THE BASICS Derived units can be broken down into more basic units Include Newtons, joules, watts
THE BASICS Prefix Notation (order of magnitude) Symbol mega kilo deci centi milli micro nano pico
Examples Which unit is 109 larger than a picometer? Which unit is 101 times smaller than a centimeter?
Complete the following 1 m = mm 1 km = m 1 m = cm 1 m = µm 1 cm = m 1 mm = m 1 m = km
Scientific Notation 0.00560 3460 2.8 x 104 8.7 x 10-5 150 x 10-9 0.0032 x 104
Practice 0.0360 87200 5.3 x 103 2.9 x 10-4 280 x 10-12 0.0045 x 105
Order of Magnitude Expresses a quantity as a power of 10 A piece of paper is about 20 cm wide. What is the order of magnitude of the width of a piece of paper in meters? The half-life of a radioisotope is 10 milliseconds. What is the order of magnitude of the half-life in seconds?
The frequency of green light is 600 THz The frequency of green light is 600 THz. What is the order of magnitude of the frequency in Hz?
Practice A commercial airplane travels at speeds of about 0.3 km/s. What is the order of magnitude of the speed of a plane in m/s?
Calculating with Numbers in Scientific Notation (6.63 x 10-34)(3 x 108) 4.5 x 10-7 (9.31 x 10-29)(3 x 108)2 (6.67 x 10-11)(5.98 x 1024)(7.35 x 1022) (3.84 x 108)2 10 = (3.0 x 10-8) X (solve for X) 1.2 x 10-2
Practice
Conversions 1 mile = 1.6 km 1 mile = 1600 meters 1 kg = 2.2 lbs 1 inch = 2.5 cm 1 lb = 453 grams 1 hour = 3600 seconds
Examples Convert 0.075 µm to m
700 mm to m 15 cm to µm
2.8 nm to mm 10 inches to cm
25 feet to meters 2.5 hours to seconds
55 miles per hour to meters per hour 48 miles per hour to meters per second
Practice a. 0.045 nm to cm b. 0.0067 meters to µm c. 18 inches to cm d. 12 hours to sec e. 10 m/s to miles per hour