1. Technical Science Scientific Tools and Methods
The Metric System
From Southwest Wisconsin Technical College

2. The Metric System In this section you will …
Describe the features of a measurement system
Describe the benefits of the Metric System
Make metric conversions
Make metric measurements

3. Measurement Systems Any measurement system will have three features.
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Measurement Systems
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Any measurement system will have three features.
Standard Units
Additional units for measuring large and small quantities
Relationships between units of measure

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Measurement Systems
Standards are units of measure that are the same no matter where you go.
A foot represents the same distance everywhere in the US. A foot is a standard unit of length.
Since everyone agrees on the value of a standard, they insure that measurements are consistent.

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Measurement Systems
You will want to make other measurements besides length. A standard is necessary for each type of measure you want to make.
Measurement English Metric
Length Foot Meter
Weight Pound Gram
Capacity Gallon Liter
etc etc etc

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Measurement Systems
A foot is a standard unit of length. But, it is not a good unit for measuring all lengths.
You could measure the room or a table in feet. But it would not make sense to measure a blood cell or the distance between two cities in feet.
A measurement system must have additional units to measure very large and very small amounts.

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Measurement Systems
What are some of the additional units of measure for length, weight, and capacity in the English system?
Length Inch, Foot, Yard, Mile, etc
Weight Ounce, Pound, Ton, etc
Capacity Cup, Pint, Quart, Gallon, Barrel, etc

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Measurement Systems
Finally, measurement systems must have relationships between the units of measure.
Since inches, feet, yards, and miles are all measurements of length then you should be able to convert from one to another.
There are 12 inches in one foot. There are 3 feet in one yard. There are 1760 yards in a mile. These relationships are constant. This allows us to convert from one unit to another.

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Measurement Systems
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What are the three requirements for a measurement system?
There must be standards for every type of measurement you want to make.
There must be additional units for measuring large and small quantities.
There must be a relationship between the units of measure.

10. Benefits of the Metric System
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Any measurement system will have three features
Standard Units
Additional units for measuring large and small quantities
Relationships between units of measure
If both the English system and the Metric system have all the requirements for a measuring system, why should we switch to the metric system?
To answer this question, let’s see how convenient the English system is to work with.

11. Benefits of the Metric System
Let’s say you were asked the following question: How many inches are in one mile?
To answer this question you would need some of the information that follows.
12 inches = 1 foot 3 feet = 1 yard
5280 feet = 1 mile 1760 yards = 1 mile
Now you can see one problem with the English system. There is no consistent relationship between the units in the English system.

12. Benefits of the Metric System
There is no consistent relationship between the units in the English system.
There are 12 inches in 1 foot. There are 3 feet in 1yard and there are 5280 feet in 1 mile.
This inconsistency makes converting in the English system very difficult for two reasons.
You have to remember all those different conversions.
Calculating with those peculiar numbers can be time consuming even with a calculator.

13. Benefits of the Metric System
The Metric system has a consistent relationship between units.
This means that as you move from one unit to the next larger or smaller you always change by the same factor.
In the Metric system the factor by which you change is 10. This makes the Metric system a base-ten system.
The next slides will explain this in more detail.

14. Benefits of the Metric System
Our monetary system is an example of a familiar base-ten system.
Dollar <=> Dime <=> Penny
As you go from one unit to the next larger or smaller, you are changing by a factor of ten.
10 pennies = 1 dime dimes = 1 dollar.
1 penny = 0.1 dimes dime = 0.1 dollars

15. Benefits of the Metric System
Converting between units in a base ten system is very easy. Dollar <=> Dime <=> Penny
To convert from a unit to the next smaller unit, multiply by 10
2 dollars = 20 dimes (2 x 10 = 20).
5 dimes = 50 pennies (5 x 10 = 50)
To convert from a unit to the next larger unit, divide by 10.
30 pennies = 3 dimes (30  10 = 3)
60 dimes = 6 dollars (60  10 = 6)

16. Benefits of the Metric System
What if you had to convert from pennies to dollars or dollars to pennies?
Dollar <=> Dime <=> Penny
Dollars and Pennies are “two positions” apart.
Each position change represents a factor of 10.
2 positions are 2 factors of 10 or 100 (10 x 10 = 100)
Multiply to convert from a larger to a smaller unit.
3 dollars = 300 pennies (3 x = 300)
Divide to convert from a smaller to a larger unit.
700 pennies = 7 dollars (700  100 = 7)

17. Benefits of the Metric System
Converting in a base ten system is just a matter of multiplying or dividing by a factor of (Factors of 10 = 10, 100, 1000, 10,000 etc.)
A fast way to multiply or divide by a factor of ten is to move the decimal.
5.623 x 100 = . . .
45.92  10 = . .
Multiply by 100, move the decimal 2 places to the right
Divide by 10, move the decimal 1 place to the left
Since the Metric System is base ten, you can convert units by simply moving the decimal point.

18. Benefits of the Metric System
Another benefit of the Metric System is the fact that that the whole world uses it. (except the US)
All fields of science use only the Metric System.
In order for a measurement system to be useful everyone must agree on the standards that make it up.
The more people that agree on those standards the better the system will be.

19. Benefits of the Metric System
You might be wondering: If the Metric system is so great why don’t we use it in the US.
The truth is that we do use the metric system.
You have probably bought a 2 liter bottle of soda
Your car has many metric parts
The aspirin you take is measured in milligrams.
The US is in the middle of a very slow process of converting to the Metric system.
As time goes by, the metric system will become a bigger part of your life.

20. Benefits of the Metric System
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Why should US companies be concerned about switching to the Metric System?
If they want to sell products to other countries they have to use their standards of measure.
It is probably more expensive to use two different measurement systems.
If some parts are produced in another country will they be compatible with parts produced here?

21. Making Metric Conversions
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Making Metric Conversions
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Study the table below to become familiar with metric units of measure.
Back

22. Making Metric Conversions
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Making Metric Conversions
Answer the following questions. Use the button below to refer to the Table of Metric Prefixes.
What is the base unit of measure for ...
Length =
Mass =
Volume =
Meter
Gram
Liter
Table

23. Making Metric Conversions
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Making Metric Conversions
Name the following units of measure. Use the prefix followed by the base unit.
1,000 meters =
0.001 liters =
0.01 meters =
10 gram =
Kilometer
Milliliter
Centimeter
Dekagram
Table

24. Making Metric Conversions
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Making Metric Conversions
You probably noticed that the metric prefixes stay the same no matter what unit of measure you use.
Length in the English system is measured in inches, feet, yards, miles etc. but volume is measured in ounces, cups, quarts, gallons, etc.
In the metric system kilo is always 1,000 base units. It doesn’t matter what you are measuring.
1000 grams is a kilogram. There are a lot less metric units to remember.
This is another benefit of the Metric System.
Table

25. Making Metric Conversions
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Making Metric Conversions
Name the unit when given the abbreviation and vice versa. Metric abbreviations use small case letters and no periods.
km = Mililiter =
mg = Kilogram =
cm = Decimeter =
Dekagram =
Kilometer
Milligram
Centimeter
Megagram
Microgram ml kg dm
dag
Table

26. Making Metric Conversions
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Making Metric Conversions
Now that you are familiar with metric units, you can make some conversions.
To make conversions within the Metric System, you have to answer two questions.
First, how many positions is it from the starting unit to the unit you want to convert to? Since the metric system is base ten, this tells how many places to move the decimal.
Second, are you converting from a larger unit to a smaller unit or from a smaller unit to a larger unit? This tells which way to move the decimal.

27. Making Metric Conversions
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Making Metric Conversions
4.5 kilometers = meters. . . . .
It is 3 positions from the starting unit (kilo) to the unit we want to convert to (base unit - meter).
We are converting from a larger unit to a smaller unit.
We need more small units than large units to make up the same amount of distance.
This means moving the decimal three places to the right.

28. Making Metric Conversions
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Making Metric Conversions
8.3 grams = milligrams. . . . .
It is 3 positions from the starting unit (gram) to the unit we want to convert to (milli).
We are converting from a larger unit to a smaller unit.
We need more small units than large units to make up the same amount of mass.
This means moving the decimal three places to the right.

29. Making Metric Conversions
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Making Metric Conversions
25,000 centimeters = kilometers. . . . . . .
It is 5 positions from the starting unit (centi) to the unit we want to convert to (kilo).
We are converting from a smaller unit to a larger unit.
We need fewer large units than small units to make up the same amount of distance.
This means moving the decimal five places to the left.

30. Making Metric Conversions
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Making Metric Conversions
75 milliliters = liters
7 5 . . . .
It is 3 positions from the starting unit (milli) to the unit we want to convert to (base unit - liter).
We are converting from a smaller unit to a larger unit.
We need fewer large units than small units to make up the same amount of volume.
This means moving the decimal three places to the left.

31. Making Metric Conversions
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Making Metric Conversions
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Make the following metric conversions.
1,000 grams = kg
500 mg = g
2.25 liters = ml
0.07 g = kg
1 kilometer = m
450 ul = ml
650 cm = m
0.30 kg = mg 1
0.5
2250
1000
0.450
750,000
6.5
300,000
Table

32. Making Metric Measurements
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Making Metric Measurements
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Now you can make metric conversions but can you answer the questions below?
You need 5 kilograms of potatoes from the store, can you carry them or should you take your car?
A label on a bottle of cough syrup reads give 5 milliliters as needed. Will 5 milliliters fit in a teaspoon or will you need a tablespoon?
You are running a 1600 meter race. Is this a sprint or a distance event?

33. Making Metric Measurements
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Making Metric Measurements
Using the metric system isn’t just about converting. You need to have a “feel” for the size of units you are working with.
The English system is familiar to you. You have an idea about how heavy 5 pounds is but you probably don’t have that same feeling for 5 kilograms.
The best way to get familiar with the metric system is to use it to make measurements.

34. Making Metric Measurements - Length
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Making Metric Measurements - Length
The following are approximations to help you get a feel for metric units of length. We will deal only with the most common units.
1 kilometer  Just over one half mile
1 meter  Just over one yard
1 centimeter  Width of your little fingernail
1 millimeter  Thickness of your fingernail

35. Making Metric Measurements - Length
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Making Metric Measurements - Length
Choose the most appropriate measure.
Length of a football field
1 km, m, 10 cm, 100 mm
Length of a newborn baby
0.5 m, km, 5,000mm, 50 cm
Thickness of a sheet of paper
0.1 mm, cm, m, 1 km,

36. Making Metric Measurements - Length
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Making Metric Measurements - Length
The diagram below is part of a metric tape measure. The numbered divisions are centimeters. The small divisions are millimeters 96 97 98 99
1 m 1 2 3 4
How many millimeters are in 1 cm?
How many centimeters are in 1 m?
Is the diagram drawn to scale?
Are the units too large or too small?
10 Millimeters
100 Centimeters No
Too large

37. Making Metric Measurements - Length
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Making Metric Measurements - Length A 96 97 98 99
1 m 1 2 3 4
Measure Line A in mm, cm, and m. (Hint: make your initial measurement in mm then convert.)
You have gone 99 cm and 2 mm.
99 cm = 990 mm
+ 2 mm
992 mm =>
99.2 cm =>
0.992 m

38. Making Metric Measurements - Length
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Making Metric Measurements - Length B 96 97 98 99
1 m 1 2 3 4
Measure Line B in mm, cm, and m.
You have gone 1 m, 2 cm, and 7 mm.
1m = 100 cm = mm
2 cm = mm
+ 7 mm
1027 mm =>
102.7 cm =>
1.027 m

39. Making Metric Measurements - Length
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Making Metric Measurements - Length 1 2 96 97 98 99
1 m 1 2 3 4
Measure Line 1 and 2 in mm, cm, and m.
Line 1 =
Line 2 =
1004 mm =>
100.4 cm =>
1.004 m
979 mm =>
97.9 cm =>
0.979 m

40. Making Metric Measurements - Length
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Making Metric Measurements - Length 3 4 96 97 98 99
2 m 1 2 3 4
Measure Line 3 and 4 in mm, cm, and m.
Line 3 =
Line 4 =
2015 mm =>
201.5 cm =>
2.015 m
1998 mm =>
199.8 cm =>
1.998 m

41. Making Metric Measurements - Mass
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Making Metric Measurements - Mass
The following are approximations to help you get a feel for metric units of mass. We will deal only with the most common units.
1 kilogram  Just over 2 pounds
1 gram  Mass of a raisin
1 milligram  Mass of a grain of sand

42. Making Metric Measurements - Mass
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Making Metric Measurements - Mass
Choose the most appropriate measure.
Mass of a nickel
50 g, 5 mg, kg, 5 g, 500 mg
Mass of an aspirin
500 mg, mg, g, 50 kg, 50 g
Mass of an average adult
700 kg, g, mg, 7,000 g, 70 kg
Mass of a baseball
400 mg, g, 4 kg, g, g

43. Making Metric Measurements - Mass
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Making Metric Measurements - Mass
Mass is measured using a balance. The object to be measured is placed in one pan and standard mass units are placed in the other pan.
50g ?
20g
10g
How many milligrams are in 1 g?
How many grams are in 1 kg?
1000 Milligrams
1000 Grams

44. Making Metric Measurements - Mass
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Making Metric Measurements - Mass
50g A
20g
10g
Measure Object A in g, mg, and kg.
Put standard mass units in the pan until it balances.
50 g
+ 20 g
+ 10 g
80 g =>
80,000 mg =>
0.080 kg

45. Making Metric Measurements - Mass
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Making Metric Measurements - Mass
50g
50g B
10g
Measure Object B in g, mg, and kg.
Put standard mass units in the pan until it balances.
50 g
+ 50 g
+ 10 g
110 g =>
110,000 mg =>
0.110 kg

46. Making Metric Measurements - Mass
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Making Metric Measurements - Mass
50g
50g 1
20g
10g
Measure Object 1 in g, mg, and kg.
Put standard mass units in the pan until it balances.
Object 1 =
130 g =>
130,000 mg =>
0.130 kg

47. Making Metric Measurements - Mass
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Making Metric Measurements - Mass
50g 2
10g
Measure Object 2 in g, mg, and kg.
Put standard mass units in the pan until it balances.
Object 2 =
60 g =>
60,000 mg =>
0.060 kg

48. Making Metric Measurements - Volume
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Making Metric Measurements - Volume
The following are approximations to help you get a feel for metric units of volume. We will deal only with the most common units.
1 liter  Just over 1 quart
1 milliliter  About 20 drops

49. Making Metric Measurements - Volume
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Making Metric Measurements - Volume
Choose the most appropriate measure.
Volume of a car’s gas tank
50 l, 5 l, ml, 50 ml, 500 l
Volume of a teaspoon
0.5 l, ml, 5 l, 5 ml, ml
Volume of a can of soda
500 l, l, ml, ml, ml
Volume of a syringe
0.02 ml, ml, l, 2 l, 2 ml

50. Making Metric Measurements - Volume
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Making Metric Measurements - Volume
Volume can be measured using beakers that are designed to hold a standard amount of fluid.
250 ml
500 ml
750 ml
1000 ml
50 ml
100 ml
100 ml
200 ml
How many milliliters are in 1 liter?
Do the small divisions represent the same volume on each beaker?
1000 Milliliters
False

51. Making Metric Measurements - Volume
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Making Metric Measurements - Volume
250 ml
500 ml
750 ml
1000 ml
Measure the volume of water in the beaker in ml and l
There are 5 divisions between 0 ml and 250 ml.
Each division is 50 ml (250  5).
You have gone past 500 ml and 2 more divisions.
500 ml
2 divisions = 100 ml
600 ml =>
0.6 liters

52. Making Metric Measurements - Volume
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Making Metric Measurements - Volume
Measure the volume of water in the beaker in ml and l
50 ml
100 ml
There are 5 divisions between 0 ml and 50 ml.
Each division is 10 ml (50  5).
You have gone past 50 ml and 4 more divisions.
50 ml
4 divisions = 40 ml
90 ml =>
0.09 liters

53. Making Metric Measurements - Volume
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Making Metric Measurements - Volume 1
Measure the volume of water in Beakers 1 & 2 in ml and l
100 ml
200 ml
Beaker 1 =
Beaker 2 =
60 ml =>
0.06 liters 2
850 ml =>
0.850 liters
250 ml
500 ml
750 ml
1000 ml

54. Making Metric Measurements
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Making Metric Measurements
Now you should be able to make metric conversions and you should have some feel for size of metric units.
Getting used to the metric system doesn’t happen all at once. You need to use it.
Make note of the metric measurements that are around you.
All items in the grocery store have metric measures.
Your car’s speedometer has a metric scale
Your tape measure and kitchen measuring cups have both a Metric and an English scale

55. Making Metric Measurements
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Making Metric Measurements
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Name at least three benefits of the Metric System.
There is a consistent relationship between units. Prefixes stay the same.
There aren’t a lot of conversion factors to remember. It’s easy to convert.
The whole world uses it.

56. Technical Science Scientific Tools and Methods
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The Metric System