Metrics and Conversions Physics Spring 2016

Multiplying fractions review When given a problem like this: 1 x 2 = __ 5 3 how do you solve it? You multiply straight across! Do this one on your notes: 3 x 3 = __ 2 4 2 15 9 8

Cancel out if possible What about if you are given this problem: 3 x 2 = __ 4 3 You could multiply straight across and then simplify… or you could cancel out first to make the problem easier 6 12 2 3 x 2 = __ 4 3 4

Conversions Turn to your neighbor and briefly discuss what it means to convert To convert means to change from one to another But what are we converting between? Usually from one unit to another A unit is a word or abbreviation that comes after the number and describes what that number means Turn to a new neighbor and briefly discuss why you think it is important to include units with numbers 100 Vs 100 dollars vs 100 cents vs 100 miles

Conversions cont’d How many shoes do you have if you have 6 pairs of shoes? How did you figure out that you would have 12 shoes? How many roses do you have if you are given 4 dozen roses? How did you figure out that there would be 48 roses? The fact that there are 2 shoes in a pair of shoes or 12 roses in a dozen roses represent a conversion factor fractions in which the numerator is equal to the denominator, but the units are different 2 shoes 12 roses 1 pair shoes 1 dozen roses Discuss with a neighbor some other conversion factors you know of

Convert this Use a conversion factor to convert 3 hours into minutes: What is the conversion factor? There are 60 minutes in an hour so: 1hr or 60 min 60 min I hr Set up the problem 3 hr x ______ = ______ min 1 *** remember, you want to cancel hours and be left with minutes, so which of the two conversion factors will you use? 60 min 180 1 hr

Convert this: Use a conversion factor to convert 360 minutes into hours: What is the conversion factor? Set up the problem 1 hr . 60 min 1 hr 360 = 6 hrs 360 min x ______ = ______ 1 60 min 60

Convert this: Use a conversion factor to convert 96 inches into feet: 96 in x 1 ft = 96 = 8 ft 1 12 in 12

2 step conversions Convert 3 yards into inches 3 yrds x 36 in = 108 inches 1 1 yrd

What does this have to do with science? METRICS!!!! Turn to a neighbor and discuss what you remember/know about metrics Used for different scientific measurements Based on the number “10” Base units: Mass – gram Volume – liter Distance (length) - meter

Metric terms Prefixes are words or parts of words that come “before” another word or word part Metric prefixes: Kilo (K) = 1000 m Hecto (H) = 100 m Deca (D) = 10 m Base unit = 1 m deci (d) = 1/10 m centi (c) = 1/100 m milli (m) = 1/1000 m To help you remember the prefixes in order: King Henry Died by Drinking Chocolate Milk

Conversion factors for metrics Up to this point, you have probably converted between the metric prefixes by simply moving the decimal, right? Not anymore! Now, you must use/show the correct conversion factors when converting between the various prefixes – this is called dimensional analysis Conversion factors examples: 1 Km or m 1000 mm or m 1000m Km 1 m cm cm or m m cm

Let’s convert! Convert 3.5 m to cm 1. What is the correct conversion factor? 1m or 100 cm 100 cm 1m 2. Solve the problem 3.5 m x 100 cm = ________ cm 1 1 m ** Which conversion factor will allow you to correctly cancel your starting units and leave you with the correct ending units? ** 350

We’ll work one together Covert 2.56 mm to m 1. What is the correct conversion factor? 2. Set up the problem and solve 1 m . 1000 mm 2.56 mm x 1 m = 2.56 = 0.00256 m 1 1000 mm 1000

Your turn! Convert 3.4 Km to m 3.4 Km x 1000 m = 3400 m 1 1 Km

A bit more difficult 125000 cm Convert 1.25 Km to cm Can you go directly from Km to cm? No, you have to do this in two steps so you need two conversion factors 1. 1 Km or 1000 m 1000m 1 Km 2. 1 m or 100 cm 100 cm 1 m Solve the problem 1.25 Km x 1000 m x 100 cm = 1 1 Km I m ** Which conversion factor will allow you to correctly cancel your starting units and leave you with the correct ending units? ** 125000 cm

Work it together Covert 3.2 mm to Km 1. What is the correct conversion factor? 2. Set up the problem and solve 1 m and 1 Km 1000 m 1000 Km 3.2 mm x 1 m x 1 Km = 1 1000 mm I 000m 0.0000032 Km

On your own Convert 9 Km to cm 9 Km x 1000 m x 100 cm = 900000 cm

Now go back to your measuring activity and complete the third column by converting the measurements to the given unit!

This is too easy…. 1 1 2.2222 1 60 60 So let’s make it a bit harder Can you convert 8km/hr into m/s? Of course you can – this is called a double conversion Where you are converting two different units in the same problem The key to solving these is to convert the units separately 8Km x m x hr x min = m/s 1 hr Km min s 1000 1 1 2.2222 1 60 60

Let’s do another one together Convert 575 Km/hr to cm/min 575Km x x x = 1 hr cm/min 1000 m 100 cm 1 hr 1 Km 1 m 60 min 958333.333

One more for good measure Convert 2500 cm/sec to m/min 2500 cm x 1 m x 60 sec = 1500 m/min 1 sec 100 cm 1 min