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Dimensional Analysis Part III. Unit conversions with two SI unit prefixes Dimensional Analysis III. Unit Prefixes Typical problem: The wavelength of green light is 500nm,what is this in millimeters? The wavelength of green light is 500nm,what is this in millimeters? Steps to solve 1. Identify starting units 2. Identify ending units 3. Identify two unit conversion factors that connects starting and ending units to the same intermediate unit (usually the base unit) 4. Arrange conversion factors in an equation so they cancel the starting unit and intermediate unit, and leave only to the final unit (No numbers) 5. Put in the numbers and solve the equation The wavelength of green light is 500nm,what is this in millimeters? Step 1. Identify starting units nm (nanometers) The wavelength of green light is 500nm,what is this in millimeters? Step 2. Identify ending units mm (millimeters) The wavelength of green light is 500nm,what is this in millimeters? 3. Identify two unit conversion factors that connects starting and ending units to the same intermediate unit (usually the base unit) Start nm (nanometers) nano milli n m End mm (millimeters) .000000001 .001 10-9 10-3 The wavelength of green light is 500nm,what is this in millimeters? nano milli n m .000000001 .001 10-9 10-3 1 nm = 1 nm 1 nm = 1x10-9 m 1 mm = 1 mm 1 mm = 1x10-3 m The wavelength of green light is 500nm,what is this in millimeters? 4. Arrange conversion factors in an equation so they cancel the starting unit and intermediate unit, and leave only to the final unit (No numbers) nm m nm mm m mm The wavelength of green light is 500nm, how many meters is this? Step 5: Put in actual numbers and solve the problem 9 1x10 m 500 nm 1 nm 1 mm 3 1x10 m 500 x10 6 mm Practice Problems The next four pages have practice problems. Work through the problems and see if you are doing them right I have a 1.44 MB (megabyte) floppy disk drive on my computer. How many Gigabytes of data will it hold? Step 1: Starting Unit Mb (Megabyte) Step 2: Ending Unit Gigabyte Step 3: Unit conversion Mega(M) = 109 Giga (G) = 1012 1 Mbyte = 1 Mbyte; 1Mbyte=1x109 byte 1 Gbyte = 1 Gbyte; 1 Gbyte=1x1012 byte Step 4: Equation Mbyte x (byte/Mbyte) x (Gbyte/byte) = byte Step 5: Solve 1.44 Mbyte x (1x109 byte/1 Mbyte) x (1Gbyte/1x1012byte) = 1.44x10-3 Mbyte How many milliliters (ml) is 16 μL? Step 1: Starting Units :l (microliters) Step 2: Ending Units millliLiters (mL) Step 3: Conversion Factor μ=10-6 m=10-3 1μL =1μL 1 mL=1 mL 1μL =1x10-6 L 1mL = 1x10-3 L Step 4: Equation 1μL x (L/μL) x (ml/L) = mL Step 5: Solve 16μL x (1x10-6 L/1μL) x (1ml/1x10-3 L) = 16x10-3 ml = .016 ml I am going to hike 56.710 kilometers. What is this in centimeters? Step 1: Starting Units kilometers (km) Step 2: Ending Units Centimeters (cm) Step 3: Conversion Unit Kilo (k) = 103 1 km = 1 km 1 km = 1x103 m Step 4: Equation centi(c) = 10-2 1 cm = 1 cm 1 cm = 1x10-2 m km x (m/km) x (cm/m) = cm Step 5: Solve 56.710 km x (1x103 m/1 km) x (1 cm/1x10-2 m)= 56.710 x 10+5 cm A solution has a concentration of 85 mM. What is the micromolar (μM) concentration of this solution? Step 1: Starting Units mM (micromolar) Step 2: Ending Units μM (micromolar) Step 3: Conversion factor m(milli) = 10-3 μ(micro) = 1x10-6 1 mM = 1 mM 1μM = 1 μM 1 mM = 1x10-3 M 1μM = 1x10-6 M Step 4: Equation mM x (M/mM) x (μM/M) = μM Step 5: Solve 85 mM x (1x10-3 M/mM) x (1 μM/1x10-6 M)= 8.5x10+3 M