Metrics and Conversions Physics Fall 2015 Multiplying fractions

Metrics and Conversions Physics Fall 2015

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

Cancel out if possible � What about if you are given this problem: 6 3 x 2 = __ 4 3 12 � You could multiply straight across and then simplify… � or you could cancel out first to make the problem easier 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: 1. What is the conversion factor? �There are 60 minutes in an hour so: 1 hr or 60 min I hr 2. Set up the problem 60 min = ______ 180 min 3 hr x ______ 1 hr 1 *** remember, you want to cancel hours and be left with minutes, so which of the two conversion factors will you use?

Convert this: � Use a conversion factor to convert 360 minutes into hours: 1. What is the conversion factor? 60 min 1 hr 2. Set up the problem 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 1000 m cm or m m Km m cm 1000 mm or 1 m m cm

Let’s convert! � Convert 3. 5 m to cm 1. What is the correct conversion factor? ** Which conversion factor will 1 m or 100 cm allow you to correctly cancel your 100 cm 1 m starting units and leave you with the correct ending units? ** 2. Solve the problem 350 3. 5 m x 100 cm = ____ cm 1 1 m

We’ll work one together � Covert 2. 56 mm to m 1. What is the correct conversion factor? 1000 mm 1 m 2. Set up the problem and solve 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 � 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 ** Which conversion factor will 1000 m 1 Km allow you to correctly cancel your 2. 1 m or 100 cm starting units and leave you with the correct ending units? ** 100 cm 1 m � Solve the problem 1. 25 Km x 1000 m x 100 cm = 125000 cm 1 1 Km Im

Work it together � Covert 3. 2 mm to Km 1. What is the correct conversion factor? 1000 mm and 1000 m 1 Km 2. Set up the problem and solve 3. 2 mm x 1 Km = 0. 0000032 Km 1 1000 mm I 000 m

On your own � Convert 9 Km to cm 9 Km x 1000 m x 100 cm = 900000 cm 1 1 Km 1

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

This is too easy…. � So let’s make it a bit harder ◦ Can you convert 8 km/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 8 Km x 1000 m x 1 hr x 1 Km 60 min 1 hr 1 min = 2. 2222 m/s 60 s

Let’s do another one together � Convert 575 Km/hr to cm/min 575 Km x 1 hr 1000 m 1 Km x 100 cm x 1 m 1 hr 60 min 958333. 333 cm/min =

One more for good measure � Convert 2500 cm/sec m/min