On July 23, 1983, Air Canada Flight 143, a Boeing 767 jetliner, ran out of fuel at an altitude of 12,500 metres (41,000 ft)

Metric-Metric conversions Conversions have never been so easy!

The SI units and other metric units can be modified by prefixes The SI units and other metric units can be modified by prefixes. Most SI units have no prefix (except for kg). An added prefix modifies the unit by some numbers (integers) of orders of magnitude.

Order of magnitude? One order of magnitude is 10. Moving up one order of magnitude is moving 10x up (or 101). Moving down is moving (1/10)x down (10-1) Two orders of magnitude is 100 (102). Moving up 2 orders of magnitude is 100x or down is 10-2x (1/100 x).

To convert metric units from one prefix to another… Determine how your units will change by moving up or down orders of magnitude. The numerical value of your measurement will change in the opposite magnitude that your unit changed. If you moved up for your units, move down for your number the same order of magnitude.

Prefix (abbrev.) Magnitude kilo (k) 103 hecto (h) 102 deka (da) 101 no prefix 1 (100) deci (d) 10-1 centi (c) 10-2 milli (m) 10-3 ------ 10-4 10-5 micro (µ) 10-6 10-7 10-8 nano (n) 10-9

Example: Convert 235.5 mm to meters. Prefix (abbrev.) Magnitude kilo (k) 103 hecto (h) 102 deka (da) 101 no prefix 1 (100) deci (d) 10-1 centi (c) 10-2 milli (m) 10-3 ------ 10-4 10-5 micro (µ) 10-6 10-7 10-8 nano (n) 10-9 Move units up 3 orders of magnitude to make mmm

Example: Convert 235.5 mm to meters. Prefix (abbrev.) Magnitude kilo (k) 103 hecto (h) 102 deka (da) 101 no prefix 1 (100) deci (d) 10-1 centi (c) 10-2 milli (m) 10-3 ------ 10-4 10-5 micro (µ) 10-6 10-7 10-8 nano (n) 10-9 Move number down 3 orders of magnitude 235.5 to 235.5 x 10-3 m

Example: Convert 235.5 mm to meters. Prefix (abbrev.) Magnitude kilo (k) 103 hecto (h) 102 deka (da) 101 no prefix 1 (100) deci (d) 10-1 centi (c) 10-2 milli (m) 10-3 ------ 10-4 10-5 micro (µ) 10-6 10-7 10-8 nano (n) 10-9 Adjust your decimal/exponent so number is in proper sci. notation. 235.5 x 10-3 m = 2.355 x 10-1 m

How to expertly convert between units Dimensional analysis How to expertly convert between units

Dimensional Analysis Method to convert from one unit of measurement into another, relying on the facts that… Multiplying any number by one does not change its value Units are treated just like numbers in mathematical operations (they can be canceled out) Meter x meter = meter2, and meter/meter = 1

One-step Unit conversions Example: convert 150.5 mph into km/hr Express your measurement as a fraction (put the number over 1), including the units. If complex units have a component in the denominator, place it there. 150.5 mph=150.5 mi hr = 150.5 mi 1 hr

Multiply your measurement by a unit conversion factor that will cancel out the units you are trying to get rid of. Units conversion factors are fractions that equal to one but have different units and numbers in the numerator and denominator. One number is usually 1. Example: given: 1 mi = 1.609344 km exactly 1 mi 1.609344 km or 1.609344 km 1 mi

Cancel units and calculate. 150.5 mi 1 hr ∗ 1.609344 km 1 mi = 242.2 km/hr

Multi-step conversions Sometimes many conversion factors are needed to get to an answer. Find out what you have and what units you want to get. Plan how you will link the units with conversion factors. (example: yrsdayshrmin, etc.) If a unit is placed in the denominator of one unit conversion factor, it will be placed in the numerator of the following conversion factor, and vice versa.

example Convert 60.0 mph to m/s 1 mile = 1.609344 km (exactly) 60.0 miles 1.609 km 1000 m 1 hour 1 mile 1 km 3600 sec