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Lab Objectives

At the conclusion of the lab, the student should be able to:

- describe the advantages of the metric system
- convert units from base units of length, mass and volume
- make predictions about the best units to use for various examples (for example, to measure a cell’s length would the student use meters or micrometers?)
- record the measurement (either length, weight, or volume) of an item

Things you should be able to explain to someone else after this lab:

- Celcius
- Volume
- Mass
- Meter
- Gram
- Length
- Area
- Temperature
- Liter

## Slideshow

A SlideShare element has been excluded from this version of the text. You can view it online here: pb.libretexts.org/bio1lm/?p=132

## Introduction

Measurements in science use **metric **units. The metric system was developed in France in 1791 so that scientists had a common unit for research comparisons. In 1960 the metric system became the basis for the International System of Units (**SI **units). The basic units of these measurements for the metric system are listed in the chart below.

Unit | Metric Measure | Abbreviation |
---|---|---|

Length | Meter | m |

Volume | Liter | L |

Mass | Gram | g |

Temperature | Celcius | ºC |

Larger or smaller units are created by adding prefixes to the terms above. The metric system is based on units of 10, so conversions from one unit to another are relatively easy and can be completed by moving a decimal point either adding or subtracting zeros.

Prefix | Symbol | Multiplier | Notation |
---|---|---|---|

pico | p | 0.000000000001 | 10^{−12} |

nano | n | 0.000000001 | 10^{−9} |

micro | µ | 0.000001 | 10^{−6} |

milli | m | 0.001 | 10^{−3} |

centi | c | 0.01 | 10^{−2} |

deci | d | 0.1 | 10^{−1} |

Base unit | g, m, or L | 1 | 10^{0} |

deka | da | 10 | 10^{1} |

hecto | h | 100 | 10^{2} |

kilo | k | 1000 | 10^{3} |

mega | M | 1000000 | 10^{6} |

giga | G | 1000000000 | 10^{9} |

tera | T | 1000000000000 | 10^{12} |

The chart on the previous page had some common metric prefixes from smallest to largest. Remember that the base unit, like a gram or a meter, is the same as 10^{0} or 1.

### Now it’s time to practice!

Make the following metric conversions:

- 1 meter = __________ centimeters = __________ millimeters
- 56.2 millimeters = __________ meters = __________ centimeters
- 13 kilometers = __________ meters = __________ decimeters
- 16 ml = __________ µl 2. 7 g = __________ mg
- 9 µl = __________ L 4. 2.3 µl = __________ mL
- 32 mm = __________ nm 6. 19 m = __________ km
- 28 m = __________ km 8. 400 ml = __________ L
- 2 kg = __________ mg 10. 82 cm = __________ km

## Part 1: Length and Area

Length is measured with a metric ruler, a meter stick, or a measuring tape. The basic unit of length is **meters**. Examine intervals marked on the metric rulers. You should see centimeter and millimeter divisions. Use a ruler to make the following measurements making sure to include units.

- Length of the book __________.
- Width of the book __________.
- Area of the book __________.

(Area = length × width) - Diameter of a penny __________.
- Measurement of object of your choice __________.

### Lab Question

What are some potential sources of error in your measurements?

## Part 2: Volume

Volume is the space occupied by an object. Units of volume are cubed (i.e. three dimensional) units of length. The **liter **(L) is the basic metric unit of volume.

- Measure and pour 50 mL water into a 100 mL graduated cylinder. Notice how the water is curved. This is called the
**meniscus**and is due to surface tension and adhesion of water molecules to the sides of the cylinder. When measuring liquids in a cylinder always get eye level with the meniscus and read the volume at the lowest level of the curve. - Fill a glass test tube with water. Use your graduated cylinders to measure the volume of the test tube in milliliters: __________.
- Convert this volume to liters: __________.

### Lab Question

What are some potential sources of error in your measurements?

## Part 3: Micropipetting

Micropipettes are used to measure the volume of extremely small amounts of liquids. They are commonly used by researchers, hospital lab technicians, and by scientists in the food and drug industries. Micropipettes measure microliters (μl).

- How many microliters are there in a milliliter?
- How many milliliters are in a liter?
- Therefore, there are __________ microliters are in a liter.

Micropipettors come in many sizes. For example, a p200 micropippettor can pipette up to 200 μl while a p1000 can pipette up to 1000 μl, or 1 ml, of liquid. Observe the micropettors available. Note that they are adjustable.

Practice micropipetting by following the instructions below. Your instructor will also demonstrate how to use the Pipetman.

Using a p20 Pipetman:

- Set the micropipette for 15 μl by turning the dial.
- Put a tip on the micropipette by firmly pressing the micropipette down into one of the tips and then twisting slightly. Usually the tips need to remain sterile, so tips are never to be picked up and put on the micropipette.
- Hold the micropipette in the palm of your hand with your thumb on the white, round knob.
- Push the knob down to the “first stop.” (You will notice that you can push down farther but it is much more difficult. This is the “second stop.”)
- While holding the white knob down, put the tip of the micropipette into the sample and slowly release the knob. You will see the sample come up into the tip.
- To dispense the sample, move the micropipette tip to a piece of parafilm and push the knob to the first stop and then to the second stop to expel the remaining liquid. Almost all of the sample should be released onto the parafilm. Note how small the 15 μl volume is!
- You can now expel the tip into the waste by pressing the smaller white button. This is similar to the eject button on a hand-held mixer.

### Lab Question

What are some potential sources of error in your measurements?

## Part 4: Mass

The **gram **is the basic metric unit of mass. Use the electronic balance to measure the following items. Make sure that first you tare (set to zero) the balance. If you have a weigh boat, you must tare the balance with the weigh boat in place.

- Rock __________
- Penny __________
- Paperclip __________
- Convert your paperclip mass to mg __________

### Lab Question

What are some potential sources of error in your measurements?

## Part 5: Temperature

Scientists measure temperature in degrees Celsius (C). Here are some typical temperatures:

- 25ºC room temperature
- 37ºC human body temperature
- 75ºC hot coffee

Measure the following temperatures with the thermometers provided and feel with your fingers so that you have an idea of what that temperature feels like!

- Room temperature __________
- Hot bath __________
- Inside refrigerator __________
- Inside freezer __________

### Lab Question

What are some potential sources of error in your measurements?

## 17.3: Metric System Conversions - Biology

**Physical Science Pacing Guide**

· **Goal One should be incorporated throughout the curriculum.**

· **See** **DPI Physical Science High School** **Units for activities.**

· **Depending on your preference, Physics may be taught first.**

** Sequence of Physical Science**

Introduction (PSc.2.1.2) density only (measurements, scientific method, graphs)

Matter (PSc.2.1.1 PSc.2.1.2 PSc. 2.1.3)

The Atom & Periodic Table (PSc. 2.1.4 PSc. 2.1.1 PSc. 2.2.1)

Chemical Bonding (PSc. 2.2.1PSc. 2.2.2 PSc. 2.2.3)

Chemical Reactions, Acids and Bases (PSc.2.2.4 PSc.2.2.5 PSc. 2.2.6)

Motion and Force (PSc. 1.1.1 PSc. 1.1.2 PSc. 1.2.1 PSc. 1.2.3)

Work, Power and Machines (PSc. 3.1.3 PSc. 3.1.4)

Energy and Heat (PSc. 3.1.2PSc 3.1.1)

* Nuclear Energy (PSc. 2.3.1 PSc. 2.3.2)

Waves (PSc.3.2.1 PSc. 3.2.2 PSc.3.2.3 PSc. 3.2.4)

Electricity & Magnetism ( PSc. 3.3.1 PSc. 3.3.2 PSc. 3.3.3 PSc. 3.3.4 PSc. 3.3.5)

## 17.3: Metric System Conversions - Biology

**Metric-English System Conversions**

1 inch (in.) = 2.54 centimeters (cm)

1 centimeter (cm) = 0.3937 inch (in.)

1 meter (m) = 3.2808 feet (ft) = 1.0936 yard (yd)

1 mile (mi) = 1.6904 kilometer (km)

1 kilometer (km) = 0.6214 mile (mi)

1 cubic inch (in. 3 ) = 16.39 cubic centimeters (cm 3 or cc)

1 cubic centimeter (cm 3 or cc) = 0.06 cubic inch (in. 3 )

1 cubic foot (ft 3 ) = 0.028 cubic meter (m 3 )

1 cubic meter (m 3 ) = 35.30 cubic feet (ft 3 ) = 1.3079 cubic yards (yd 3 )

1 fluid ounce (oz) = 29.6 milliliters (mL) = 0.03 liter (L)

1 milliliter (mL) = 0.03 fluid ounce (oz) = 4 teaspoon (approximate)

1 pint (pt) = 473 milliliters (mL) = 0.47 liter (L)

1 quart (qt) = 946 milliliters (mL) = 0.9463 liter (L)

1 gallon (gal) = 3.79 liters (L)

1 liter (L) = 1.0567 quarts (qt) = 0.26 gallon (gal)

1 square inch (in. 2 ) = 6.45 square centimeters (cm 2 )

1 square centimeter (cm 2 ) = 0.155 square inch (in. 2 )

1 square foot (ft 2 ) = 0.0929 square meter (m 2 )

1 square meter (m 2 ) = 10.7639 square feet (ft 2 ) = 1.1960 square yards (yd 2 )

## Damped Vibrations

With the model just described, the motion of the mass continues indefinitely. Clearly, this doesn&rsquot happen in the real world. In the real world, there is almost always some friction in the system, which causes the oscillations to die off slowly&mdashan effect called *damping*. So now let&rsquos look at how to incorporate that damping force into our differential equation.

Physical spring-mass systems almost always have some damping as a result of friction, air resistance, or a physical damper, called a *dashpot* (a pneumatic cylinder Figure (PageIndex<4>)).

Figure (PageIndex<4>): A dashpot is a pneumatic cylinder that dampens the motion of an oscillating system.

Because damping is primarily a friction force, we assume it is proportional to the velocity of the mass and acts in the opposite direction. So the damping force is given by (&minusbx&prime) for some constant (b>0). Again applying Newton&rsquos second law, the differential equation becomes

Then the associated characteristic equation is

Applying the quadratic formula, we have

Just as in Second-Order Linear Equations we consider three cases, based on whether the characteristic equation has distinct real roots, a repeated real root, or complex conjugate roots.

### Case 1: Overdamped Vibrations

When (b^2>4mk), we say the system is ** overdamped**. The general solution has the form

where both (&lambda_1) and (&lambda_2) are less than zero. Because the exponents are negative, the displacement decays to zero over time, usually quite quickly. Overdamped systems do not oscillate (no more than one change of direction), but simply move back toward the equilibrium position. Figure (PageIndex<5>) shows what typical critically damped behavior looks like.

Figure (PageIndex<5>): Behavior of an overdamped spring-mass system, with no change in direction (a) and only one change in direction (b).

Example (PageIndex<3>): Overdamped Spring-Mass System

A 16-lb mass is attached to a 10-ft spring. When the mass comes to rest in the equilibrium position, the spring measures 15 ft 4 in. The system is immersed in a medium that imparts a damping force equal to 5252 times the instantaneous velocity of the mass. Find the equation of motion if the mass is pushed upward from the equilibrium position with an initial upward velocity of 5 ft/sec. What is the position of the mass after 10 sec? Its velocity?

The mass stretches the spring 5 ft 4 in., or (dfrac<16><3>) ft. Thus, (16=(dfrac<16><3>)k,) so (k=3.) We also have (m=dfrac<16><32>=dfrac<1><2>), so the differential equation is

Multiplying through by 2 gives (x&Prime+5x&prime+6x=0), which has the general solution

Applying the initial conditions, (x(0)=0) and (x&prime(0)=&minus5), we get

After 10 sec the mass is at position

so it is, effectively, at the equilibrium position. We have (x&prime(t)=10e^<&minus2t>&minus15e^<&minus3t>), so after 10 sec the mass is moving at a velocity of

After only 10 sec, the mass is barely moving.

A 2-kg mass is attached to a spring with spring constant 24 N/m. The system is then immersed in a medium imparting a damping force equal to 16 times the instantaneous velocity of the mass. Find the equation of motion if it is released from rest at a point 40 cm below equilibrium.

Follow the process from the previous example.

### Case 2: Critically Damped Vibrations

When (b^2=4mk), we say the system is *critically damped*. The general solution has the form

where (&lambda_1) is less than zero. The motion of a critically damped system is very similar to that of an overdamped system. It does not oscillate. However, with a critically damped system, if the damping is reduced even a little, oscillatory behavior results. From a practical perspective, physical systems are almost always either overdamped or underdamped (case 3, which we consider next). It is impossible to fine-tune the characteristics of a physical system so that (b^2) and (4mk) are exactly equal. Figure (PageIndex<6>) shows what typical critically damped behavior looks like.

Figure (PageIndex<6>): Behavior of a critically damped spring-mass system. The system graphed in part (a) has more damping than the system graphed in part (b).

Example (PageIndex<4>): Critically Damped Spring-Mass System

A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from equilibrium with an upward velocity of 3 m/sec.

We have (mg=1(9.8)=0.2k), so (k=49.) Then, the differential equation is

which has general solution

Applying the initial conditions (x(0)=0) and (x&prime(0)=&minus3) gives

A 1-lb weight stretches a spring 6 in., and the system is attached to a dashpot that imparts a damping force equal to half the instantaneous velocity of the mass. Find the equation of motion if the mass is released from rest at a point 6 in. below equilibrium.

First find the spring constant.

### Case 3: Undamped Vibrations

When (b^2<4mk), we say the system is *underdamped*. The general solution has the form

where (&alpha) is less than zero. Underdamped systems do oscillate because of the sine and cosine terms in the solution. However, the exponential term dominates eventually, so the amplitude of the oscillations decreases over time. Figure (PageIndex<7>) shows what typical underdamped behavior looks like.

Figure (PageIndex<7>): Behavior of an underdamped spring-mass system.

Note that for all damped systems, ( lim limits_

Example (PageIndex<5>): Underdamped Spring-Mass System

A 16-lb weight stretches a spring 3.2 ft. Assume the damping force on the system is equal to the instantaneous velocity of the mass. Find the equation of motion if the mass is released from rest at a point 9 in. below equilibrium.

We have (k=dfrac<16><3.2>=5) and (m=dfrac<16><32>=dfrac<1><2>,) so the differential equation is

This equation has the general solution

[x(t)=e^ <&minust>( c_1 cos (3t)+c_2 sin (3t) ) . onumber]

Applying the initial conditions, (x(0)=dfrac<3><4>) and (x&prime(0)=0,) we get

[x(t)=e^ <&minust>igg( dfrac<3> <4>cos (3t)+ dfrac<1> <4>sin (3t) igg) . onumber]

A 1-kg mass stretches a spring 49 cm. The system is immersed in a medium that imparts a damping force equal to four times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from rest at a point 24 cm above equilibrium.

First find the spring constant.

Example (PageIndex<6>): Chapter Opener: Modeling a Motorcycle Suspension System

For motocross riders, the suspension systems on their motorcycles are very important. The off-road courses on which they ride often include jumps, and losing control of the motorcycle when they land could cost them the race.

Figure (PageIndex<8>): (credit: modification of work by nSeika, Flickr)

This suspension system can be modeled as a damped spring-mass system. We define our frame of reference with respect to the frame of the motorcycle. Assume the end of the shock absorber attached to the motorcycle frame is fixed. Then, the &ldquomass&rdquo in our spring-mass system is the motorcycle wheel. We measure the position of the wheel with respect to the motorcycle frame. This may seem counterintuitive, since, in many cases, it is actually the motorcycle frame that moves, but this frame of reference preserves the development of the differential equation that was done earlier. As with earlier development, we define the downward direction to be positive.

When the motorcycle is lifted by its frame, the wheel hangs freely and the spring is uncompressed. This is the spring&rsquos natural position. When the motorcycle is placed on the ground and the rider mounts the motorcycle, the spring compresses and the system is in the equilibrium position (Figure (PageIndex<9>)).

Figure (PageIndex<9>): We can use a spring-mass system to model a motorcycle suspension.

This system can be modeled using the same differential equation we used before:

A motocross motorcycle weighs 204 lb, and we assume a rider weight of 180 lb. When the rider mounts the motorcycle, the suspension compresses 4 in., then comes to rest at equilibrium. The suspension system provides damping equal to 240 times the instantaneous vertical velocity of the motorcycle (and rider).

- Set up the differential equation that models the behavior of the motorcycle suspension system.
- We are interested in what happens when the motorcycle lands after taking a jump. Let time [t=0] denote the time when the motorcycle first contacts the ground. If the motorcycle hits the ground with a velocity of 10 ft/sec downward, find the equation of motion of the motorcycle after the jump.
- Graph the equation of motion over the first second after the motorcycle hits the ground.

- We have defined equilibrium to be the point where (mg=ks), so we have

Therefore, the differential equation that models the behavior of the motorcycle suspension is

Dividing through by 12, we get

Now, to determine our initial conditions, we consider the position and velocity of the motorcycle wheel when the wheel first contacts the ground. Since the motorcycle was in the air prior to contacting the ground, the wheel was hanging freely and the spring was uncompressed. Therefore the wheel is 4 in. ((dfrac<1><3> ext

NASA is planning a mission to Mars. To save money, engineers have decided to adapt one of the moon landing vehicles for the new mission. However, they are concerned about how the different gravitational forces will affect the suspension system that cushions the craft when it touches down. The acceleration resulting from gravity on the moon is 1.6 m/sec 2 , whereas on Mars it is 3.7 m/sec 2 .

The suspension system on the craft can be modeled as a damped spring-mass system. In this case, the spring is below the moon lander, so the spring is slightly compressed at equilibrium, as shown in Figure (PageIndex<11>).

Figure (PageIndex<11>): The landing craft suspension can be represented as a damped spring-mass system. (credit &ldquolander&rdquo: NASA)

We retain the convention that down is positive. Despite the new orientation, an examination of the forces affecting the lander shows that the same differential equation can be used to model the position of the landing craft relative to equilibrium:

where (m) is the mass of the lander, (b) is the damping coefficient, and (k) is the spring constant.

- The lander has a mass of 15,000 kg and the spring is 2 m long when uncompressed. The lander is designed to compress the spring 0.5 m to reach the equilibrium position under lunar gravity. The dashpot imparts a damping force equal to 48,000 times the instantaneous velocity of the lander. Set up the differential equation that models the motion of the lander when the craft lands on the moon.
- Let time (t=0) denote the instant the lander touches down. The rate of descent of the lander can be controlled by the crew, so that it is descending at a rate of 2 m/sec when it touches down. Find the equation of motion of the lander on the moon.
- If the lander is traveling too fast when it touches down, it could fully compress the spring and &ldquobottom out.&rdquo Bottoming out could damage the landing craft and must be avoided at all costs. Graph the equation of motion found in part 2. If the spring is 0.5 m long when fully compressed, will the lander be in danger of bottoming out?
- Assuming NASA engineers make no adjustments to the spring or the damper, how far does the lander compress the spring to reach the equilibrium position under Martian gravity?
- If the lander crew uses the same procedures on Mars as on the moon, and keeps the rate of descent to 2 m/sec, will the lander bottom out when it lands on Mars?
- What adjustments, if any, should the NASA engineers make to use the lander safely on Mars?

## Measurement - The Metric System - Easy Conversions 1

*This Math quiz is called 'Measurement - The Metric System - Easy Conversions 1' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

*It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us*

As you know, everything in life involves math in one form or another. Growing up in the United States, you have been taught the American or English system of math. However, most of the rest of the world does not use this system. Rather, they use the **metric system**.

You may not even realize it but you have already been exposed to the metric system. Pick up any can of vegetables or a bag of cookies and you will notice two different measurement amounts listed. You will see ounces or pounds and you will also see grams. When you buy soda, do you buy a pint of soda or a half gallon or soda or a gallon of soda? No, you buy soda in liters. Grams and liters are part of the metric system.

The metric system is really a very easy system to learn. It is easy because it works in base 10 conversions. This is true for each type of measurement such as for length or distance, known as **meters**, mass or weight, known as **grams**, and volume, known as **liters**. However, to be able to convert in the system, you do need to memorize the order of the system. To help you with that, memorize the following little phrase.

Have a look at the phrase and further explanation in purple below before tackling the questions.

## Metric conversions & US customary unit conversion calculator

### Metric Converter Calculator Choose measurement units:

Area square/squared units square inches to square feet, square meters. | Speed mph to kph, ft/sec. |

Currency converter money, dollars, euros. | Temperature celsius to fahrenheit |

Distance meter to foot, mile to kilometer. | Time hours to minutes, days to years. |

Length / Height centimeter to inch, feet, meter. | Volume cubic/cubed units,liters in a gallon |

Power watts, kw, horsepower, calories | Weight kilogram to pound, ounce, mg. |

Pressure psi, atmospheres, millimeter of mercury | Fruit |

Fuel economy | |

Fractions to decimals | |

Metric Conversion Factors Chart This easy-to-use metric conversion table includes standard conversion factors for common units and measurements. |

#### Learn More

Math For Real Life

Examples for everyday situations.

Pocket Ref

A concise reference for virtually any subject.

#### Metric Conversion Questions?

A unit of measurement is a defined magnitude of a particular quantity, which is used as a standard. Any other quantity of that same kind can be expressed as a multiple of the unit of measurement.

Measurement is the process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.

Different systems of units are based on different choices of a set of base units. The most widely used system of units is the International System of Units, or SI (sometimes referred to as the Metric System).

## Metric Unit Conversion Worksheets

We often come across situations where we need to bring a uniformity in the units, this is when converting between units comes into play. Learning metric units have a whole lot of advantages, it's simple as it's units scale to the power of 10. Trigger some interesting practice along the way with this huge compilation of metric unit conversion worksheets comprising a conversion factors cheat sheet, and exercises to convert metric units of length, mass or weight, and capacity. The resources here cater to the learning requirements of grade 3, grade 4, grade 5, and grade 6. Our free sample worksheets are sure to leave kids yearning for more!!

Memorize a handful of conversion formulas from this printable metric unit conversion cheat sheet. Look up the formulas until you get a hang of them. Try this mnemonic "King Henry Died Drinking Chocolate Milk" to remember the prefixes in order.

Comprehend the relationship between the metric units of length such as millimeters (mm), centimeters (cm), and meters (m). Practice converting from one metric unit of length to the other like a pro with these pdfs for 3rd grade, 4th grade, and 5th grade kids.

Distance traveled is measured in meters and kilometers, and the need to convert between the two arises quite often. Get conversion savvy with our printable handouts on converting between meters (m) and kilometers (km).

Learn this magic spell: 10 mm = 1 cm, 100 cm = 1 m, and 1000 m = 1 km, and multiply to convert from larger units of length to smaller and divide to do vice versa in these pdf worksheets on converting metric units.

Determine the relationship between the units: grams and kilograms to polish up your conversion skills. Multiply by 1000 to convert the mass measures in kg to g, and divide them by 1000 to convert from g to kg.

Multiplying or dividing the weight by an appropriate power of ten is all that your kids do, as they page through our printable worksheets on converting metric units of weight.

Determine if the learning objective has been met with this set of revision worksheets for grade 5 and grade 6 on converting metric units of weight featuring a mix of units such as grams, kilograms, and metric tons.

Capacity comes next in the ladder of metric unit conversions. Converting from milliliters to liters and liters to milliliters is no more a tough nut to crack, as learners walk through these practice sheets.

Assessment is the key component of learning. Stock up your resources with these pdf exercises to review or test the knowledge of grade 4 and grade 5 students in converting metric units of liquid volume.

## Inches

Use of the inch can be traced back as far as the 7th century. The first explicit definition we could find of its length was after 1066 when it was defined as the length of three barleycorns. This was not a satisfactory reference as barleycorn lengths vary naturally. The British Standards Institute defined the inch as 25.4mm in 1930 in the document "Metric Units in Engineering: Going SI". In March 1932 the American Standards Association were asked to rule on whether to adopt the same value (at the time the American inch was 1/.03937 mm which approximated to 25.400051 mm). Because the values were so close, and because Britain has already settled on that value, the ASA adopted this value on March 13, 1933.

## The Metric System

The **metric system** is a standardized system of measurement used by scientists throughout the world. It is also the measurement system used in everyday life in most countries. Although the metric system is the only measurement system ever acknowledged by Congress, the United States remains "out of step" with the rest of the world by clinging to the antiquated English system of measurements involving pounds, inches, and so on.

Metric units commonly used in biology include

Unlike the English system with which you are already familiar, the metric system is based on units of ten, thus simplifying interconversions (table B.1). This base-ten system is similar to our monetary system, in which 10 cents equals a dime, 10 dimes equals a dollar, and so on. Units of ten in the metric system are indicated by Latin and Greek prefixes placed before the base units:

For example, 620 g = 0.620 kg = 620,000 mg = 6,200 dg = 62,000 cg.

#### Units of Length

The **meter** (m) is the basic unit of length.

Units of area are squared (i.e., two-dimensional) units of length:

The following comparisons will help you appreciate these conversions of length and area:

Measurements of area and volume can use the same units:

The following comparisons will help you appreciate these conversions of volume:

#### Units of Mass

The **gram** is the basic unit of mass.

The following comparisons will help you appreciate these conversions of mass:

Remember that mass is not necessarily synonymous with weight. Mass measures an object&rsquos potential to interact with gravity, whereas weight is the force exerted by gravity on an object. Thus, a weightless object in outer space has the same mass as it has on earth.

#### Units of Volume

The **liter** (L) is the basic unit of volume. A typical thermos bottle holds about 1 liter a standard flush toilet flushes about 20 liters of water. Units of volume are cubed (i.e., three-dimensional) units of length.

#### Units of Temperature

You are probably most familiar with temperature measured with the Fahrenheit scale, which is based on water freezing at 32°F and boiling at 212°F. Celsius temperatures are synonymous with Centigrade temperatures, and these scales measure temperature in the metric system. Celsius (°C) temperatures are easier to work with than Fahrenheit temperatures since the Celsius scale is based on water freezing at 0°C and boiling at 100°C. You can interconvert °F and °C with the following formula:

#### Celsius versus Centigrade

The Celsius temperature scale was developed in 1742 by Anders Celsius, a Swedish astronomer. Interestingly, Celsius originally set 0°C as the boiling point of water and 100°C as the freezing point of water. Soon thereafter, J. P. Christine revised the scale to its present form&mdashwith 0°C as the freezing point and 100°C as the boiling point of water. The Celsius scale is identical to the Centigrade scale.

The following comparisons will help you appreciate the conversions of Fahrenheit and Centigrade temperatures:

#### Hints for Using the Metric System

- Express measurements in units requiring only a few decimal places. For example, 0.3 m is more easily manipulated and understood than 300,000,000 nm.
- When measuring water, the metric system offers an easy and common conversion from volume measured in liters to volume measured in cubic meters to mass measured in grams: 1 mL = 1 cm 3 = 1 g.
- Familiarize yourself with manipulations within the metric system. Work within one system, and do not convert back and forth between the metric and English systems.
- The metric system uses symbols rather than abbreviations. Therefore, do not place a period after metric symbols (e.g., 1 g, not 1 g.). Use a period after a symbol only at the end of a sentence.
- Do not mix units or symbols (e.g., 9.2 m, not 9 m, 200 mm).
- Metric symbols are always singular (e.g., 10 km, not 10 kms).
- Except for degree Celsius, always leave a space between a number and a metric symbol (e.g., 20 mm, not 20mm 10°C, not 10°C).
- Use a zero before a decimal point when the number is less than one (e.g., 0.42 m, not .42 m).

The following site contains interesting information and an on-line tutorial about the metric system:

**Prefix Division of Metric Unit Equivalent Prefix Multiple of Metric Unit Equivalent (Latin) (meter) (Greek) (meter)**

deci (d) 0.1 10 -1 (tenth part), deka (da) 10 10 1 (tenfold)

centi (c) 0.01 10 -2 (hundredth part), hecto (h) 100 10 2 (hundredfold)

milli (m) 0.001 10 -3 (thousandth part), kilo (k) 1,000 10 3 (thousandfold)

micro (µ) 0.000001 10 -6 (millionth part), mega (M) 1,000,000 10 6 (millionfold)

nano (n) 0.000000001 10 9 (billionth part), giga (G) 1,000,000,000 10 9 (billionfold)

pico (p) 0.000000000001 10 -12 (trillionth part), tera (T) 1,000,000,000,000 10 12 (trillionfold)

## Miles to km conversion table

miles to km conversion tablemiles | km |
---|---|

1 miles | 1.609344 km |

2 miles | 3.218688 km |

3 miles | 4.828032 km |

4 miles | 6.437376 km |

5 miles | 8.046720 km |

6 miles | 9.656064 km |

7 miles | 11.265408 km |

8 miles | 12.874752 km |

9 miles | 14.484096 km |

10 miles | 16.093440 km |

20 miles | 32.186880 km |

30 miles | 48.280320 km |

40 miles | 64.373760 km |

50 miles | 80.467200 km |

60 miles | 96.560640 km |

70 miles | 112.654080 km |

80 miles | 128.747520 km |

90 miles | 144.840960 km |

100 miles | 160.934400 km |

Unit conversion tables like the above can be useful if for some reason you don't have access to an online converter.

#### References:

[1] NIST Special Publication 330 (2008) - "The International System of Units (SI)", edited by Barry N.Taylor and Ambler Thompson

[2] International Organization for Standardization (1993). ISO Standards Handbook: Quantities and units (3rd edition). Geneva: ISO. ISBN 92-67-10185-4.

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