Metric and Conversions Mark Ewoldsen, Ph.D. La Cañada High School

Units and Measurement Physics Mrs. Coyle http://apod.nasa.gov/apod/image/0706/iss_sts117_big.jpg

SI Unit Prefixes - Part I Name Symbol Factor tera- T 1012 giga- G 109 mega- M 106 kilo- k 103

SI Unit Prefixes- Part II Name Symbol Factor centi- c 10-2 milli- m 10-3 micro- μ 10-6 nano- n 10-9 pico- p 10-12 femto- f 10-15

Basic Physics – SI Units Quantity Unit Symbol Length meter m Mass kilogram kg Time second S Volume liter L

Derived SI Units (examples) Quantity Unit Symbol Speed meter per second m/s Newton kg m/ s2 N Energy Joule (kg m2/s2) J Pressure Pascal (kg/(ms2) Pa

SI Unit Prefixes for Length Name Symbol gigameter Gm 109 1000 Mm megameter Mm 106 1000 km kilometer km 103 1000 m centimeter cm 10-2 millimeter mm 10-3 1000 μm micrometer μm 10-6 1000 nm nanometer nm 10-9 1000 pm picometer pm 10-12

M x 10n M En Scientific Notation M is the coefficient 1<M<10 or M En M is the coefficient 1<M<10 10 is the base n is the exponent or power of 10

Other Examples: 5.45E+6 or 5.45 x 10^6

Numbers less than 1 will have a negative exponent. A millionth of a second is: 0.000001 sec 1x10-6 1.0E-6 1.0^-6

Solving Word Problems Analyze List knowns and unknowns. Draw a diagram. Devise a plan. Write the math equation to be used. Calculate If needed, rearrange the equation to solve for the unknown. Substitute the knowns with units in the equation and express the answer with units. Evaluate Is the answer reasonable?

Unit Conversions Dr. John Mattox Department of Chemistry and Physics Fayetteville State University 1200 Murchison Rd. Fayetteville, NC 28301

We start by writing down the Converting Inches to centimeters 10.0 in cm = We start by writing down the number and the units

Converting Inches to centimeters 10.0 in 2.54 cm cm = 1 in Our conversion factor for this is 1 in = 2.54 cm. Since we want to convert to cm, it goes on the top.

Converting Inches to centimeters 10.0 in 2.54 cm cm = 1 in Now we cancel and collect units. The inches cancel out, leaving us with cm – the unit we are converting to.

Converting Inches to centimeters 10.0 in 2.54 cm 25.4 cm = 1 in The Since the unit is correct, all that is left to do is the arithmetic... The Answer

Even though we have two different numbers and two different units, they represent the exact same length. You can check this by looking at a ruler – find the 10 in mark and directly across at the cm side. What number do you find?

A more complex conversion km to m hr s In order to work a NSCI 110 homework problem, we need to convert kilometers per hour into meters per second. We can do both conversions at once using the same method as in the previous conversion.

A more complex conversion km to m hr s Step 1 – Write down the number and the unit! 80 km hr

A more complex conversion km to m hr s 80 km 1 hr m = s hr 3600 s First we’ll convert time. Our conversion factor is 1 hour = 3600 sec. Since we want hours to cancel out, we put it on the top.

A more complex conversion km to m hr s 80 km 1 hr 1000 m m = s hr 3600 s 1 km Next we convert our distance from kilometers to meters. The conversion factor is 1 km = 1000 m. Since we want to get rid of km, this time it goes on the bottom.

A more complex conversion km to m hr s 80 km 1 hr 1000 m m = s hr 3600 s 1 km Now comes the important step – cancel and collect units. If you have chosen the correct conversion factors, you should only be left with the units you want to convert to.

A more complex conversion km to m hr s 80 km 1 hr 1000 m = hr 3600 s 1 km 80,000 m Since the unit is correct, we can now do the math – simply multiply all the numbers on the top and bottom, then divide the two. 3600 s

A more complex conversion km to m hr s 80 km 1 hr 1000 m = hr 3600 s 1 km 80,000 m m s 22 The Answer!! = 3600 s

both velocities. A car that is exact same velocity as a car 80 km/hr and 22 m/s are both velocities. A car that is moving at a velocity of 80 km/hr is traveling the exact same velocity as a car traveling at 22 m/s.