# Drill – 9/20 How many seconds are in 9.7 hours?

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Drill – 9/20 How many seconds are in 9.7 hours?
2. How did you figure out that answer?

SI Units, Metric Conversions, & Dimensional Analysis

A major theme of science is communication and collaboration
A major theme of science is communication and collaboration. We need a single measurement system for everyone. Le Systeme International d’Unites - SI

SI UNITS Quantity Unit Name Abbreviation Length Meter m Mass Kilogram
kg Time Second s Temperature Kelvin K Amount of substance Mole mol Electric current Ampere A Luminous intensity Candela cd

We use SI prefixes to represent quantities that are larger or smaller than the base units.

Prefix Abbreviation Conversion giga G 1 Gm = 109 m mega M 1 Mm = 106 m kilo k 1 km = 1000 m hecto h 1 hm = 100 m deca da 1 dam = 10 m 1 meter (1 m) deci d 1 m = 10 dm centi c 1 m = 100 cm milli m 1 m = 1000 mm micro μ 1 m = 106 μm nano n 1 m = 109 nm

Dimensional Analysis Dimensional Analysis is a method used to make conversions. This method helps us organize information without becoming confused about what units are being cancelled or multiplied/divided.

Everything on bottom is divided from the top
Rules You must use Dimensional Analysis to solve conversion problems Always show all your work Include units Make sure your units cancel out Everything on the top is multiplied Everything on bottom is divided from the top

Conversion Factors A ratio (or fraction) derived from the equality between two different units that can be used to convert from one unit to the other. Conversion factors always equal one because the two values are equal to each other.

Conversion Factors 4 quarters 1 dollar = 1 = 1 1 dollar 4 quarters
60 minutes 1 hour = 1 = 1 1 hour 60 minutes 1 m 100 cm = 1 = 1 100 cm 1 m

Convert 62.0 inches to centimeters
First we need to map out what we are doing. 62.0 in  ___ cm

Convert 62.0 inches to centimeters
Second we need to determine our conversion factor How many centimeters are in one inch? 2.54 cm = 1 in 1 in 2.54 cm Note: We could have also used that 1cm = .394 inch but as a general rule, the larger unit gets the 1! = 1 = 1 2.54 cm 1 in

Convert 62.0 inches to centimeters
Third, we multiply our given by the conversion factor…making sure to arrange the conversion factor so that the units CANCEL! 62.0 in 2.54 cm X = cm 1 in Note: Units that are both on the top and the bottom cancel

Convert 62.0 inches to centimeters
Lastly, we make sure that we reached our “destination” and that we have the correct number of significant figures. cm  157 cm Note: Conversions factors do not follow significant figure rules, they are not measured and do not show accuracy.

Multiple Conversions When conversions require several steps, Dimensional Analysis is extremely useful. It helps organize information so we can think through problems step-by-step.

How many feet are in 965 cm? 1. Map it out: 965 cm  ___ ft
2. Find conversion factors:

How many feet are in 965 cm? 965 cm 1 in 1 ft X X = 31.66  31.7 ft

You are cooking for a large group of people
You are cooking for a large group of people. You must change the recipe to accommodate all the guests. How many gallons will 384 teaspoons of vanilla extract occupy? 1 Tablespoon (T) = 3 teaspoons (t) 1 cup (c) = 16 Tablespoons 1 pint (pt) = 2 cups 1 quart (qt) = 2 pints 1 gallon (gal) = 4 quarts

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