The Metric System. J. Montvilo

Transcription

1 The Metric System J. Montvilo 1

2 Measuring Systems There are two major measuring systems in use: The English System and The Metric System Which do you prefer and why? 2

3 Measuring Systems Assuming you prefer the English System to the Metric System, let s find out how much you really know about it. Take out a piece of paper 3

4 Pop Quiz on the English System All the answers relate to the English System of measurement. 4

5 Pop Quiz on the English System Question 1: How many barleycorns are there in a foot? 5

6 Pop Quiz on the English System Question 2: Why is the elbow called the elbow? (And, no, it is not because it is shaped like the letter L!) 6

7 Pop Quiz on the English System Question 3: Which is heavier, a pound of feathers or a pound of gold? 7

8 Pop Quiz on the English System Extra Credit: Which is heavier, an ounce of feathers or an ounce of gold? 8

9 Pop Quiz on the English System Quick Review of the Questions: 1. How many barleycorns are there in a foot? 2. Why is the elbow called the elbow? 3. Which is heavier, a pound of feathers or a pound of gold? E.C. Which is heavier, an ounce of feathers or an ounce of gold? 9

10 Pop Quiz: The Answers But first Any measuring system needs standards to measure length, space taken up, amounts, and so forth. These artificial standards can be based on many things, and in the past the standards were often based on things like seed length or the size of body parts of kings. So 10

11 Pop Quiz: The Answers Question 1: How many barleycorns are there in a foot? Based one of the standards of the day, an inch was equal to the width of a king s thumb knuckle (and a foot was the length of his foot, and so on). Rather than having to keep being measured, one of the kings (Edward II, 1324) pronounced that one inch would be equal to three barleycorns laid end to end. 11

12 Pop Quiz: The Answers So, what is a barleycorn? It is simply a grain of barley (a barley grain). (In England, grain is called corn, and corn is called maize.) 12

13 Pop Quiz: The Answers Therefore, if one inch is three barleycorns in length and a foot has twelve inches there must be 36 barleycorns in a foot. How many barleycorns are there in a yard? There are 3 feet (36 inches) in a yard, so there are 108 barleycorns in a yard. 13

14 Pop Quiz: The Answers Question 2: Why is the elbow called the elbow? First, what is a bow? It s a bend, an arc, as in a bow (and arrow) or a rainbow. 14

15 Pop Quiz: The Answers Second, what is an el? Actually, what is an ell? An ell is a unit of measurement equal to the distance from the fingers of an outstretched arm to well, that depends. 15

16 Pop Quiz: The Answers There are different kinds of ells, depending on where you are from. 16

17 Pop Quiz: The Answers In any case, the elbow is the bow [bend] in the ell. 17

18 Pop Quiz: The Answers Question 3: Which is heavier, a pound of feathers or a pound of gold? No, they are not the same. Common items, like feathers are measured in the Avoirdupois subsystem of the English System; there are 16 ounces per pound in this system. Precious metals, like gold, are measured in the Troy subsystem of the English System; there are 12 ounces per pound in this system. 18

19 Pop Quiz: The Answers So, a pound of feathers is heavier than a pound of gold. Troy Avoirdupois 19

20 Pop Quiz: The Answers EC: Which is heavier, an ounce of feathers or an ounce of gold? No, they are not the same. The ounce (437.5 grains) in the Avoirdupois subsystem of the English System is smaller than the ounce (480 grains) in the Troy subsystem. (But 12 Troy ounces still weigh less than 16 Avoirdupois ounces.) 20

21 Pop Quiz: The Answers So, an ounce of gold is heavier than an ounce of feathers. (But a pound of feathers is heavier than a pound of gold.) Troy Avoirdupois 21

22 Pop Quiz: The Answers Confusing, isn t it? barleycorns, 3, 12, 36, different standards in different places, and so on. Can it be made simpler? Yes. And it was. 22

23 The Metric System: Some History The French Revolution ( ): What was it all about? 23

24 The Metric System Standards Metric System standards are based on naturally-occurring things that could be measured by anyone; presumably they do not change (like seed size or people do). The basic standard is for length, and other standards can be derived from that. How was the standard for length derived? 24

25 The Metric System Standards: Length The distance between the north pole and the equator was measured. 25

26 The Metric System Standards: Length One ten-millionth ( 1 /10,000,000) of that distance was defined as one meter. 26

27 The Metric System Prefix Standard Examples 1 meter m m 27

28 The Metric System Standards: Length To make smaller units, just divide the standard into ten parts. Then give each part a name, but base it on a standard prefix before the standard name that tells you what you did to the standard in this case deci- ( 1 /10); one meter contains 10 decimeters. 28

29 The Metric System Prefix Standard Examples 1 meter m m, dm 1 / deci- d 29

30 The Metric System Standards: Length If that unit is too large, you make smaller units by dividing the unit into ten smaller parts, thereby, in this case, dividing the entire meter into 100 smaller parts. Give each part a name, based on a standard prefix before the standard name that tells you what you did to the standard in this case centi- ( 1 /100); one meter contains 100 centimeters. 30

31 The Metric System Prefix Standard Examples 1 meter m m, dm, cm 1 / / deci- centi- d c 31

32 The Metric System Standards: Length If that unit is too large, you make smaller units by dividing each unit into ten smaller units, thereby dividing the meter into 1000 smaller parts. Then give each part a name based on the standard prefix before the standard that tells you what you did to the standard in this case milli- ( 1 /1000); one meter contains 1000 millimeters. 32

33 The Metric System Prefix Standard Examples 1 meter m m, dm, cm, mm 1 / / / deci- centi- milli- d c m 33

34 The Metric System Standards: Length Need smaller units? Keep going. Divide the standard by 1,000,000 (micro-) or divide the standard by 1,000,000,000 (nano-), or 34

35 The Metric System Prefix Standard Examples 1 meter m m, dm, cm, mm, µm 1 / / / deci- centi- milli- d c m 1 / micro- µ 35

36 The Metric System Standards: Length What if you need larger units? Just multiply the standard by 10 (deka-), or 100 (hecto-), or 1000 (kilo-), or 1,000,000 (mega-), or 1,000,000,000 (giga-), or 36

37 The Metric System Prefix Standard Examples 1000 kilo- k 1 meter m m, dm, cm, mm, µm km 1 / / / deci- centi- milli- d c m 1 / micro- µ 37

38 The Metric System Standards: Area Area is a two-dimensional measurement; it is a length times a width. 38

39 The Metric System Standards: Volume (Space) Volume is a three-dimensional (cubic)measurement; it is a length times a width times a height (or some related measures). 39

40 The Metric System Standards: Volume (Space) To create a standard, you can begin with cube that is 1 cm by 1 cm by 1 cm in size (1 cubic centimeter [1 cc] or 1 cm 3 ). But that is fairly small. 40

41 The Metric System Standards: Volume (Space) So, multiply that volume by 1000 and you get 1000 cubic centimeters, or one liter, which is the standard for volume. 41

42 The Metric System Prefix Standard Examples 1000 kilo- k 1 meter m m, dm, cm, mm, µm km 1 / deci- d liter L L 1 / centi- c 1 / milli- m 1 / micro- µ 42

43 The Metric System Standards: Volume (Space) What if you need something larger or smaller? Just multiply or divide by the appropriate power of ten. For example: 1 /1000 of a liter is a milliliter (1 ml) 1 /1,000,000 of a liter is a microliter (1 µl) 1000 liters is a kiloliter (1 kl) and so forth. 43

44 The Metric System Prefix Standard Examples 1000 kilo- k 1 meter m m, dm, cm, mm, µm km 1 / / deci- centi- d c liter L L, dl, cl, ml, µl kl 1 / milli- m 1 / micro- µ 44

45 The Metric System Standards:Volume (Space) What is the difference between 1 cc (1 cubic centimeter; 1 cm3) and 1 ml? 1 cc 1 ml But the correct metric name is Nothing; they are both 1/1000 of a liter. one milliliter. 45

46 The Metric System Standards: Mass What does one liter of water weigh? 2.2 pounds (on Earth). What does weigh mean? What would that same amount of water weigh on the moon? 0.37 pounds. 46

47 The Metric System Standards: Mass What would that same amount of water weigh on Mars? 0.84 pounds What would that same amount of water weigh on Jupiter? 5.50 pounds. What would that same amount of water weigh in orbit around Earth? 0 pounds (more or less). 47

48 The Metric System Standards: Mass What kind of standard is weight if it changes from place to place? What didn t change? The amount of water that is, basically, its mass did not change. So why not use mass as the standard? It is. 48

49 The Metric System Standards: Mass By definition, one liter of pure water has a mass of 1 kilogram. But that is pretty big. So, 1 /1000 of a kilogram is used as the standard for mass; it is equal to one gram. If you need to measure smaller or larger amounts, just use the appropriate multiple of the gram. 49

50 The Metric System Prefix Standard Examples 1000 kilo- k 1 meter m m, dm, cm, mm, µm km 1 / / deci- centi- d c liter L L, dl, cl, ml, µl kl 1 / milli- m 1 / micro- µ gram g g, dg, cg, mg, µg kg 50

51 The Metric System And that is the basics of the Metric System: a standard and a prefix that tells what you did to that standard. Know those and you know most of what you need to know. The rest is just practice, which is what this lab is about. One (or two) more things 51

52 The Metric System Standards: Temperature What is your normal body temperature? You MUST place units with the measurement: degrees You MUST tell what scale was used: F (or C) What does F mean? [After Daniel Fahrenheit ( )] What does C mean? [After Anders Celsius ( )] 52

53 The Metric System: Converting How do you convert between the English System and the Metric System? Try not to. But, if you have to, just use the formulas that are available. 53

54 The Metric System: Converting How do you convert within the Metric System? There are many ways, but one easy way is to use equivalences. For example: 1 m is equivalent to 100 cm 100 cm is equivalent to 1 m 1 m is equivalent to 1000 mm 1000 mm is equivalent to 1 m 1 m = 100 cm = 1000 mm 54

55 The Metric System: Converting Example 1: How many millimeters are in 4.6 meters? 1 m = 1000 mm (they are equivalent) Whatever mathematical process you apply to one side of the equation you can apply to the other side and they are still equivalent. 4.6 x 1 m = 1000 mm x 4.6 therefore 4.6 m = 4,600 mm 55

56 The Metric System: Converting Example 2: How many liters are in 756 milliliters? 1 ml = L (they are equivalent) Whatever mathematical process you apply to one side of the equation you can apply to the other side and they are still equivalent. 756 x 1 ml = L x 756 therefore 756 ml = L 56

57 The Metric System Why should you know the Metric System? First, it is used in science, and this is a science course, so Second, outside of science, it is used almost everywhere else in the world, so 57

58 The Metric System Any Questions? 58