Metric Prefixes Tera- T 10 2 centi- c 10 9 Giga- G 10 3 milli- m 10 6 Mega- M 10 6 micro- µ 10 3 kilo- k 10 9 nano- n

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1 Metric Prefixes Meaning Name Abbreviation Meaning Name Abbreviation Tera- T 10 2 centi- c 10 9 Giga- G 10 3 milli- m 10 6 Mega- M 10 6 micro- µ 10 3 kilo- k 10 9 nano- n These are the most commonly used metric prefixes. You should commit them to memory.

2 Unit Conversions In solving mathematical equations that contain measurements, it is necessary that all the units of measurement be consistant. For example, one should not mix centimeters and meters within the same calculation. An easy way to make the necessary conversions is to use the powers of 10 notation. 6.7 km = m In this way, all the measurements of length within the same problem can be expressed in terms of meters.

3 Unit Consistency All of these conversions become possible with a working knowledge of the meanings of the metric prefixes 8.7 cm = m 756 nm = m = m 1300 kg = m = m 980 cm/s 2 = m/s 2 = 9.8 m/s 2

4 Relationships between units There are 100 centimeters in a meter. There are 4 quarts in a gallon. These common expressions can be written mathematically. 100 cm = 1 m 4 qt. = 1 gallon

5 Conversion Factors They can also be written as ratios. 1 m 100 cm 1 gallon 4 quarts or 100 cm 1 m or 4 quarts 1 gallon Which way you write them depends upon what you want to do with them.

6 Conversion Factors in Use Here's a sample problem that makes use of such a conversion factor: Problem: Convert 7.5 meter to centimeters. 7.5 m 100 cm 1 m =750 cm In this case, we write 1 m in the denominator because we wish to cancel the units m and replace them with cm.

7 Conversion Factors in Use Here's another sample problem: Problem: Convert 5.0 centimeters to meters. 5.0 cm 1 m 100 cm =0.050 m In this case, we write 100 cm in the denominator because we wish to cancel the units cm and replace them with m.

8 Conversion Factors in Use Problem: Convert 9.2 millimeters to centimeters. 9.2 mm 1 cm 10 mm =0.92 cm 10 mm appears in the denomenator because there are 10 mm in one centimeter. The overall value of any conversion factor is unity because whatever is written in the numerator is equivalent to what is in the denominator.

9 Converting Non-metric Units Problem: Convert 672 seconds to minutes. 672 s 1 min 60 s =11.2 min If you accidently write the conversion factor the wrong way, the units won't cancel and the answer looks rediculous. 672 s 60 s 1 min =40320 min But 672 seconds minutes!

10 More Examples Problem: Convert 11 feet to inches ft 12 in 1 ft =132 in Problem: Convert 180 sq. feet to sq. yards. 180 ft 2 1 yd2 9 ft 2 =20 yd 2

11 Metric English Conversions Problem: Convert 16 inches to centimeters in 2.54 cm 1 in =40.6 cm Problem: Convert 895 Watts to horsepower. 895 Watts 1 hp Watts =1.20 hp

12 Multiple Conversions You may insert as many conversion factors as necessary to complete the job. Problem: Convert 4 days to seconds. 4 days 24 hours 1 day 60 min 1 hour 60 s 1 min = s First we had to convert the days to hours, then the hours to minutes, and finally the minutes to seconds. In each step we had to cancel the previous units and replace them with the next.

13 Multiple Conversions In this example, we have to convert pre-existing units in both the numerator and denominator. Problem: Convert 105 km/h to m/s. 105 km h 1000 m 1 km 1 h 60 min 1 min 60 s =29.2m s Notice that the first conversion factor changes km to m. Then the second and third conversion factors change the hours to minutes and then to seconds.

14 Step-by-step Let's go thorugh a converison problem one step at a time to make sure we know what we're doing. Problem: Convert 5030 joules to Btu's. Step 1: Look up the conversion if you don't know it or are unsure. 1 Btu = 1055 joules according to the list of conversion factors found inside the front cover of the text Physics by Cutnell and Johnson.

15 Step-by-step Problem: Convert 5030 joules to Btu's. Step 2: Write the conversion as a ratio. You will decide later which version of the ratio you will actually use. 1 Btu 1055 joules or 1055 joules 1 Btu

16 Step-by-step Problem: Convert 5030 joules to Btu's. Step 3: Write the value you are given followed by an empty set of parentheses into which you will place your conversion factor. ( ) (5030 joules) =

17 Step-by-step Problem: Convert 5030 joules to Btu's. Step 4: Place the correct version of your ratio within the parentheses so that the units you want to change are cancelled. ( 1 Btu ) (5030 joules) = 1055 joules

18 Step-by-step Problem: Convert 5030 joules to Btu's. Step 5: Do the math. Write the answer with the correct units. ( 1 Btu ) (5030 joules) = 1055 joules 4.77 Btu

19 Summary Step 1: Look up the numerical value of the conversion you need. Step 2: Write the conversion as a ratio. Step 3: Write the value you are given followed by an empty set of parentheses into which you will place your conversion factor. Step 4: Place the correct version of your ratio within the parentheses so that the units you want to change are cancelled. Step 5: Do the math. Write the answer with the correct units. ( 1 Btu ) (5030 joules) = 1055 joules 4.77 Btu

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