Technical Science Scientific Tools and Methods

Technical Science

Scientific Tools and Methods

The Metric System

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

Measurement Systems

– Standard Units

– Additional units for measuring large and small quantities

– Relationships between units of measure

Any measurement system will have three features.

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Measurement Systems

– 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.

Standards are units of measure that are the same no matter where you go.

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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

– 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.

A foot is a standard unit of length. But, it is not a good unit for measuring all lengths.

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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

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.

Finally, measurement systems must have relationships between the units of measure.

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Measurement Systems

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.

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Benefits of the Metric System

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.

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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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.

Let’s say you were asked the following question: How many inches are in one mile?

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– 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.

There is no consistent relationship between the units in the English system.

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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.

The Metric system has a consistent relationship between units.

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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 10 dimes = 1 dollar.

– 1 penny = 0.1 dimes 1 dime = 0.1 dollars

Our monetary system is an example of a familiar base-ten system.

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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)

Converting between units in a base ten system is very easy. Dollar <=> Dime <=> Penny

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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 100 = 300)

Divide to convert from a smaller to a larger unit.– 700 pennies = 7 dollars (700 100 = 7)

What if you had to convert from pennies to dollars or dollars to pennies?

Dollar <=> Dime <=> Penny

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A fast way to multiply or divide by a factor of ten is to move the decimal.

Converting in a base ten system is just a matter of multiplying or dividing by a factor of 10. (Factors of 10 = 10, 100, 1000, 10,000 etc.)

Since the Metric System is base ten, you can convert units by simply moving the decimal point.

5.623 x 100 = 5 6 2 3 45.92 10 = 4 5 9 2. . . . .

– Multiply by 100, move the decimal 2 places to the right

– Divide by 10, move the decimal 1 place to the left

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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.

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.

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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.

You might be wondering: If the Metric system is so great why don’t we use it in the US.

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Benefits of theMetric System 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?

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Making Metric Conversions Home

Study the table below to become familiar with metric units of measure.

Giga (G) 1,000,000,000. (1 billion) times base unit--------------------

Mega (M) 1,000,000. (1 million) times base unit--------------------Kilo (k) 1,000. (1 thousand) times base unitHecto (h) 100. (1 hundred) times base unitDeka (dk) 10. (ten) times base unitBase Unit 1. Gram, Meter, or LiterDeci (d) 0.1 (1 tenth) times base unitCenti (c) 0.01 (1 hundredth) times base unitMilli (m) 0.001 (1 thousandth) times base unit--------------------

Micro (u) 0.000001 (1 millionth) times base unit--------------------

Nano (n) 0.000000001 (1 billionth) times base unit

Back

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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 =

Table

Meter Gram Liter

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Name the following units of measure. Use the prefix followed by the base unit.– 1,000 meters =

– 0.001 liters =

– 0.000001 grams =

– 0.01 meters =

– 10 gram =

– 1,000,000 bytes =

Kilometer Milliliter Microgram Centimeter Dekagram Megabyte

Table

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– 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. 1000 watts is a kilowatt.– There are a lot less metric units to remember.

This is another benefit of the Metric System.

You probably noticed that the metric prefixes stay the same no matter what unit of measure you use.

Table

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Name the unit when given the abbreviation and vice versa. Metric abbreviations use small case letters (except mega and giga) and no periods.– km = Mililiter =

– mg = Kilogram =

– cm = Nanometer =

– Mg = Decimeter =

– ug = Dekagram =

Kilometer Milligram Centimeter Megagram Microgram

Table

ml kg nm dm dkg

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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.

Now that you are familiar with metric units, you can make some conversions.

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4.5 kilometers = meters.

1 It is 3 positions from the starting unit (kilo) to the unit we want to convert to (base unit - meter).

2 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.

4 5 0 0. . . .

Giga (G)--------------------

Mega (M)--------------------Kilo (k)Hecto (h)Deka (dk)Base UnitDeci (d)Centi (c)Milli (m)--------------------

Micro (u)--------------------

Nano (n)

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8.3 milligrams = micrograms.

1 It is 3 positions from the starting unit (milli) to the unit we want to convert to (micro).

2 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.

– Note: the dashed lines represent positions. From milli to micro is 3 positions not 1

8 3 0 0. . . .

Giga (G)--------------------


Micro (u)--------------------

Nano (n)

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25,000 centimeters = kilometers.

1 It is 5 positions from the starting unit (centi) to the unit we want to convert to (kilo).

2 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.

2 5 0 0 0 ......0

Giga (G)--------------------


Micro (u)--------------------

Nano (n)

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Making Metric Conversions10 of 11

75 milliliters = liters

1 It is 3 positions from the starting unit (milli) to the unit we want to convert to (base unit - liter).

2 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.

7 5 .... 00Giga (G)--------------------


Micro (u)--------------------

Nano (n)


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

– 75 cm = um

– 650 cm = m

– 0.30 kg = mg

1 0.5 2250 0.00007 1000 0.450 750,000 6.5 300,000

Table

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Making MetricMeasurements 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?

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Making MetricMeasurements 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.

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Making MetricMeasurements - 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– 1 micrometer Diameter of a bacteria

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Making MetricMeasurements - Length Choose the most appropriate measure.

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Length of a football field– 1 km, 100 m, 1,000 um, 10 cm, 100 mm

Length of a newborn baby– 0.5 m, 0.05 km, 500 um, 5,000mm, 50 cm

Thickness of a sheet of paper– 0.1 mm, 0.1 cm, 0.01 m, 1 km, 10 um

Making Metric Measurements - Length The diagram below is part of a metric tape

measure. The numbered divisions are centimeters. The small divisions are millimeters

10 Millimeters 100 Centimeters No Too large

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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?

Making Metric Measurements - Length

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Measure Line A in mm, cm, and m. (Hint: make your initial measurement in mm then convert.)

96 97 98 99 1 m 1 2 3 4

A

99 cm = 990 mm + 2 mm

992 mm => 99.2 cm => 0.992 m

You have gone 99 cm and 2 mm.


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Measure Line B in mm, cm, and m.

96 97 98 99 1 m 1 2 3 4

B

1m = 100 cm = 1000 mm

+ 7 mm

1027 mm => 102.7 cm => 1.027 m

You have gone 1 m, 2 cm, and 7 mm.

2 cm = 20 mm


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Measure Line 1 and 2 in mm, cm, and m.

96 97 98 99 1 m 1 2 3 4

1

1004 mm => 100.4 cm => 1.004 m Line 1 = Line 2 =

2

979 mm => 97.9 cm => 0.979 m


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Measure Line 3 and 4 in mm, cm, and m.

96 97 98 99 2 m 1 2 3 4

3

2015 mm => 201.5 cm => 2.015 m Line 3 = Line 4 =

4

1998 mm => 199.8 cm => 1.998 m

Making MetricMeasurements - 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

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Making MetricMeasurements - Mass Choose the most appropriate measure.

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Mass of a nickel– 50 g, 5 mg, 0.5 kg, 5 g, 500 mg

Mass of an aspirin– 500 mg, 0.5 mg, 500 g, 50 kg, 50 g

Mass of an average adult– 700 kg, 0.7 g, 700 mg, 7,000 g, 70 kg

Mass of a baseball– 400 mg, 0.4 g, 4 kg, 400 g, 40 g

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.

1000 Milligrams 1000 Grams

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How many milligrams are in 1 g? How many grams are in 1 kg?

20g50g

10g?

Making Metric Measurements - Mass

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Measure Object A in g, mg, and kg.

50 g + 20 g

80 g => 80,000 mg => 0.080 kg

Put standard mass units in the pan until it balances.

20g50g

10gA

+ 10 g

50g


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Measure Object B in g, mg, and kg.

50 g + 50 g

110 g => 110,000 mg => 0.110 kg


50g10g

B

+ 10 g

20g50g


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Measure Object 1 in g, mg, and kg.

130 g => 130,000 mg => 0.130 kg


50g10g

1

Object 1 =


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Measure Object 2 in g, mg, and kg.

60 g => 60,000 mg => 0.060 kg


50g10g 2

Object 2 =

Making MetricMeasurements - 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

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Making MetricMeasurements - Volume Choose the most appropriate measure.

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Volume of a car’s gas tank– 50 l, 5 l, 500 ml, 50 ml, 500 l

Volume of a teaspoon– 0.5 l, 0.5 ml, 5 l, 5 ml, 500 ml

Volume of a can of soda– 500 l, 0.05 l, 500 ml, 0.5 ml, 0.005 ml

Volume of a syringe– 0.02 ml, 200 ml, 0.02 l, 2 l, 2 ml

Making Metric Measurements - Volume Volume can be measured using beakers that are

designed to hold a standard amount of fluid.

1000 Milliliters False

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How many milliliters are in 1 liter? Do the small divisions represent the

same volume on each beaker?

250 ml

500 ml

750 ml

1000 ml

50 ml

100 ml

100 ml

200 ml

Making Metric Measurements - Volume

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Measure the volume of water in the beaker in ml and l

500 ml 2 divisions = 100 ml

600 ml => 0.6 liters

There are 5 divisions between 0 ml and 250 ml.

Each division is 50 ml (250 5).250 ml

500 ml

750 ml

1000 ml

You have gone past 500 ml and 2 more divisions.


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Measure the volume of water in the beaker in ml and l

50 ml 4 divisions = 40 ml

90 ml => 0.09 liters

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

100 ml


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Measure the volume of water in Beakers 1 & 2 in ml and l

60 ml => 0.06 liters Beaker 1 =

Beaker 2 =

100 ml

200 ml

250 ml

500 ml

750 ml

1000 ml

850 ml => 0.850 liters

1

2

Making MetricMeasurements 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

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Making MetricMeasurements 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.

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The Metric System

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