ORDERS OF MAGNITUDE

How Big, How Long, How Far, How Fast, How Many ...
(Hint: click on the blue squares to find the answers to the purple questions)


Introduction For hundreds of years scientists have investigated the ways in which our world works and the many ways in which its workings can be described including biological, chemical, physical and so forth. For the most part the scientists observations and explanations (theories) have been descriptive but the new science - the science of the late twentieth century - has introduced a more quantitative (mathematical) aspect to science. The color red is no longer simply red but can be described in terms of its wavelength, frequency or velocity. This change in how science can explain things has come about through the development of technology which has produced tools that enable us to make such measurements.
This page presents 31 diverse measurements of how many, how big, how long, ...

1. How big is an acre? An acre was the descriptive name given in about 1300 AD to the amount of land that one man with his oxen and plough could plough in one day. This amount tended to vary since some land is easier to plough than others but now, in the U.S., one acre is 4,840 square yards; 640 acres is one square mile.
Question: Is 5 square miles the same area as five miles square?

2. How big is a barleycorn? Well, it is actually one third of an inch long (3 barleycorns = 1 inch) but this 15th Century term is rarely used these days. When the term barleycorn (meaning an actual barley corn from the middle of an ear of barley) was common, it was also general practice to consider that the weight/mass of 1 barleycorn = 1 grain. The unit 1 grain is still in common usage but without any reference to barleycorns.
Question: How many lines long was 1 barleycorn?

3. How small is a nanosecond? A nanosecond is a tiny unit of time that in the US is one billionth of a second and in the UK is one thousand-millionth of a second. (You need to remember that a billion in the US is 1,000,000,000 or one thousand-million but in the UK a billion is 1,000,000,000,000 or one million-million!)
The prefix nano, derived from the ancient Greek word meaning dwarf, reduces the unit to which it is attached to one US billionth of its standard size.
Question: Which is smaller, a nanometer or a millimeter?

4. How long is a musical note? Two crotchets equal one minim; two minims equal one semibreve; and two semibreves equal one breve. A breve is a double whole note.
These are names used in musical notation to indicate the length of time that a note is sustained.
1 breve = 2 semibreves = 4 minims = 8 crotchets.
Quantitative science has not intruded itself very much in this arena and while the relative length of musical notes in a piece of music complies with the accepted standard given above, the actual legth of the notes will depend upon the manner in which the musician plays them.
Question: Which note can also be called a quarter note?

5. How fast must a good pianist be able to play? To play some parts of an etude by Chopin a pianist needs to be able to read and play 3,950 notes in two and a half minutes. A piece (Mouvement Perpetuel) by Weber requires the pianist to play 4,541 notes in less than four minutes.
Question: Is the actual length of a quarter note always exactly the same in every piece of music or when played by all musicians?

6. How fast can a bird fly? The spine-tailed swift has been timed at 106 miles per hour (mph). The highest average speed in level flight over a long distance is probably that of a carrier pigeon which has been timed over a distance of 186 miles at 97.40 mph. The peregrin falcon can reach speeds of 180 mph when diving for its prey; and some waterflowl can fly at up to 70 mph.
Question: What is the fastest that you can walk - 1, 2, 3, or 4 mph?

7. Which animal typically travels the slowest - tortoise, snail, caterpillar, earthworm or housefly? A tortoise travels at about 5 yards/minute; the snail at 23 inches to 55 yards/hour; the earthworm at 18 yards/hour; the housefly at 5 miles/hour. The microscopic amoeba travels at less than half an inch per hour.
Question: Which is slower; 5 yards per minute, or 55 yards per hour?

8. How fast does wind blow? A cyclone moves along at 12 to 21 miles per hour (mph), but its winds are whirling around at several hundred miles an hour. The windiest place in the world is near the South Pole, the windiest place in the United States is Mount Washington in New Hampshire.
In 1806 an admiral in the British Navy devised a wind speed scale to describe the force of winds at sea. A force of 12 was a wind that no canvas could withstand. Nowadays the descriptions distinguish between land and sea and have actual wind speeds associated with them. A force 12 describes a hurricane with a wind speed overland of 73-82 miles per hour at 11 metres above the ground.
Question: What is the name of the wind scale?

9. How fast does sound travel? Sound travels at different speeds through different media. Through dry air at sea level and at freezing point (0 degrees Centigrade/Celsius), sound travels at about 5 seconds per mile. Sound travels a bit faster as the temperature of the air rises above 0 degrees Celsius but never travels anywhere near as fast as light. Can you think what natural phenomenon demonstrates this very clearly? Think about thunder and lightning storms. Which do you notice first, the light of the lightning or the sound of the thunder?
What about other media? Water is more dense than air but is more elastic and sound travels faster in water than in air. Sound cannot travel through a vacuum.
Question: What units are used in the measurement of sound intensity or pressure?

10. How fast does light travel? Light travels through the vacuum of space at 299,793 km per second (which is 1,079,252,960 km per hour); or 186,282 miles per second (which is 670,619,880 miles per hour). The speed of light is not constant; it travels about 3 percent more slowly through air and much more slowly through glass or water.
Question: Compare this with the speed of sound in air. Does sound travel through air faster than light? What natural phenomenon can you think of that would help you to answer this question?

11. How long is a day? A day is 86,400 seconds or 24 hours long which is the time it takes Earth to rotate once on its axis. This is measured by observing the movment of the Sun relative to a fixed point on Earth.
Interestingly, when we measure the length of a day by observation of the movement of a star other than the Sun, we find that the time taken by a complete rotation of Earth is shorter. This shorter day is called a sidereal day.
Question: How many minutes are there in a 24 hour solar day?

12. How long is a year? A year is the length of time that it takes Earth to make a complete revolution around the Sun. Technically this is exactly 365 days, 5 hours, 48 minutes and 45.51 seconds.
Because the measurement of the passage of time is important in the affairs of man, the period of time that we call a year has been recognized since the earliest times. At first it was probably divided up into useful chunks of time simply by noting the changing seasons. Much later, the first Roman calendar appears to have divided the year into ten months. An early Greek calendar organized the year into 12 months.
Question: What happens every four years to our modern twelve-month (365 day) calendar to account for the extra 5 hours, 48 minutes and 45.51 seconds that accumulate each year?

13. How long is it since the Age of the Dinosaurs on Earth? In late Permian times (at the end of the Paleozoic Era, about 230 million years ago) some scaly-skinned, egg laying repties evolved and gradually came to dominate animal life on Earth for many millions of years. These were the dinosaurs. It is probably about 65 million years since the last dinosaur lived on Earth. Many modern animals, including humans, had not yet evolved when the last of the dinosaurs died.
Question: For how many millions of years did dinosaurs roam the Earth?

14. How many years will an animal live? The life expectancy of a cat is between 13 and 17 years. A mouse might live for 2 to 3 years; an owl for as many as 24 years; a dolphin for 65 years; and a tortoise for perhaps 100 years. Humans may live for 70 years or more but most of the cells in a human body do not live as long as a year and have to be continually replaced. Cells on the outer layers of the skin last for between 19 and 34 days. They are continually replaced by the growth of new cells in the germinal layer of the skin. The cells of the stomach lining last for only a couple of days.
Question: For how many days do red blood cells last as they circulate around the body?

15. How many karats in pure gold? Pure gold (chemical symbol Au) is a highly valued metal that is too soft and ductile to be suitable in its pure form for jewellry such as rings or as settings for precious gems. Consequently gold is typically alloyed with silver (Ag) or copper (Cu) to make it stronger and appropriate for its intended use.
Pure gold is described as 24 karat. 18 karat gold is an alloy with 18 parts gold and 6 parts another metal.
Question: What fraction of 22 karat gold is some other metal?

16. How long does it take a common cold to develop? In medicine the time that it takes after infection by a bacterium or virus for the onset of an illness is called the incubation period. The incubation period for a common cold can be as short as 2 hours but can be up to 72 hours.
Influenza takes 2 to 3 days to develop, measles 8-13 days, and rabies 2-6 weeks.
Question: How long does it take for rubella (german measles) to devlop after an intitial infection?

17. How strong is an earthquake? Charles Richter (1900-1985), an American seismologist, created a logarithmic scale that expresses the strength of earthquake shocks. An earthquake that is only detectable by sensitive seismographic machines is strength 2.0 to 2.9; slight vibration and swinging of hanging objects is indication of a strength 3.0 to 3.9 earthquake. In a level 7.0 to 7.9 earthquake buildings collapse, cracks appear in the ground and landslides occur. The scale is a logarithmic scale and a level 4.0 earthquake is ten times stronger than a level 3.0.
Question: What is the number given to the strongest earthquake described by the Richter scale?

18. How many octaves? The word octave is used in several contexts including music, time and chemistry.
In music an octave is the eight notes that make up a chromatic (major) scale between a keynote and the next corresponding keynote up or down the scale. For example, starting with the note called middle C the following notes up to the next highest C would be D, E, F, G, A, B and C. This sequence from C to C is an octave but an octave can start on any keynote it does not have to start on a C.
Question: How many octaves can be achieved on an Oboe?

19. How many twos and threes? There are many words to express the quantity 2 (two) such as: pair, couple, brace, duo, duet, double, twosome, deuce, twofold, duplex, dual, twice, second, binary, etc.
Similarly there are many words expressing the quantity 3 (three) including: trio, triad, triplet, trilogy, trinity, threesome, triangle, tripod, threefold, thrice, treble, triple, triplex, triplicate, tripartite, ternary, third, tertiary, and so forth.
Question: What quantity is expressed by the word vicenary or vigesimal?

20. How many blood cells? The cells in mammalian blood that transport oxygen atoms around the body are the red blood corpuscles (erythrocytes). They contain hemoglobin (haemoglobin) which is the compound onto which the oxygen is attached as the blood passes through the capillaries in the lungs.
Human adult males normally will have about 5 million red blood cells in each cubic milliliter of blood.
Question: Does an adult human female normally have the same number of red blood cells per cu. milliliter as the adult human male?

21. How many ones and zeros? The number system that we are most familiar with is the base-ten decimal system. In this system the sequence of numbers is 1,2,3,4,5,6,7,8,9,10; then 11,12,13,14,15,16,17,18,19,20; etc.
There are other number systems in use and in modern computer technologies the binary system based simply on zero and one is the prevalent number system. Comparing binary with decimal numbers: 1=1, 10=2, 11=3, 100=4, 101=5, 110=6, 111=7, 1000=8.
Question: What is the decimal equivalent of the binary number 1010

22. How big is a billion? The answer to this question is not as clear cut as you might expect. Of course, everyone knows that one million is a number with six zeros and is one thousand thousand (1,000,000). But, not everyone knows (although most people do) that while the number one million is the same magnitude (size) around the world, the number one billion may not mean the same in the UK as it does in the US.
In the US one billion is always one thousand million (has 9 zeros). In the UK one billion is sometimes used to mean one million million! (has 12 zeros)
More explanation
Question: Is the number one trillion also smaller in the US than in the UK?

23. How heavy is a ton? The answer will depend upon which part of the world you are in. If you are in the US the ton weighs two thousand (2,000) pounds and is called a short ton. If you are in the UK your ton will weigh two thousand, two hundred and forty (2,240) pounds and will be called a long ton. As you can see it is very important in international dealings to make sure that you clarify just which weights and measures you are dealing with. (Fortunately, ounces and pounds weigh the same in both the US and the UK systems.)
Question: In the parts of the world using the metric system is the metric ton the same as the long ton or the short ton?

24. How much milk in a pint? And, how much petrol (gasoline) in a gallon? This will depend upon where you are! Of course pints and gallons are slowly being replaced with a universal, standard - the metric system - but until this change is completed the differences in apparently same measurements can be a problem.
In the US a pint of milk contains 16 fluid ounces and one cup of milk contains 8 fluid ounces. However, in the UK a pint of milk contains 20 fluid ounces and a cup is 10 fluid ounces!
This difference continues when we are dealing with gallons. A US gallon of gasoline has 128 fluid ounces; a UK gallon of petrol (same thing, different name!) has 160 fluid ounces.
Question: In the metric system of measurement, is one liter (or litre) of water bigger or smaller than a US pint?

25. How far is a mile? The mile was originally a Roman unit measurement of distance and was 1,000 double-paces; one Roman mile is generally considered to have been what we would now describe as 1,618 yards.
However, in the modern world one (statute) mile is longer than that, it is 1,760 yards or 5,280 feet. While this is longer than the old Roman mile, it is shorter than the old Scottish or Irish miles.
To liven up the context it is worth knowing that the word mile is used in Denmark to represent 4.7 statute miles, and in Sweden to represent 6.2 statute miles.
Question: How many furlongs are there in a statute mile?

26. How far is a sea mile? Well, while a statute mile (on land) is 1,760 yards, a nautical (at sea) mile is approximately 2,028 yards by UK standards, and approximately 2,025 yards by US standards.
Question: What is a geographical mile?

27. How fast is a knot? (There is a wonderful opportunity here for making a pun - you do it though, not us.)
A knot is a speed of one nautical mile per hour. In Britain one knot = one nautical mile per hour = 6,080 feet per hour = 1.1520 statute (on land) miles per hour
In the US one knot = 1 nautical mile per hour = 6,076.11549 feet per hour = 1.508 statute miles per hour.
Question: If a boat is travelling at 20 knots and is moving at 23.04 nautical miles per hour is it using the US or the UK system of nautical (at sea) speed?

28. How far is it From Earth to the farthest edge of our Galaxy? It is approximately 75,000 light years.
A light year is the distance that light travels through space in one year (365 days). This is a measure of distance, not of time.
1 light year = 5,880,534,262,081.1 miles;
1 light year = 9,467,660,160,950.6 kilometres
also
1 light year = 63,271.47 Astronomical Units; and
3.26 light years = 1 parsec.
Our Sun is one of perhaps 100 billion stars that occupy the Milky Way Galaxy. The Sun and planets move at a rate of about 150 miles per second around the center of the galaxy, requiring some 225 million years (one cosmic year) to complete each circuit.
Question: About how many stars are within 70 light years of Earth?

29. What units are used in the International System of Units? Because the world has developed such a variety of illogical, imprecise and confusing measurements, french scientists have devised a universal standard - the System Internationale de Unites which uses the metric system as its base. Most countries in the world (except the US) have accepted the new system and most are using it - particularly in science.
SI units are all in multiples of ten and there are seven fundamental standards: the meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), candela (light intensity), and mole (amount of substance). From the fundamental units a large number of other units are derived.
Question: In the SI system, what is measured by the joule and the hertz?

30. How many atoms? In the Periodic Table of (Chemical) Elements originally devised in 1869 by the chemist Mendeleev and augmented over the years with newly discovered elements there are more than 100 elements. (And therefore there exist over 100 types of atoms.) Under normal conditions atoms do not exist separate from each other; they are always in groups joined together as molecules. The great variety groupings of atoms into molecules provides a wonderful range of chemical substances.
In the air, the small amount of carbon dioxide present exists as molecules of carbon and oxygen joined in such a way that each molecule has one atom of carbon and two atoms of oxygen (3 atoms in each molecule). The nitrogen molecules in the air are combined in pairs; each nitrogen molecule having two nitrogen atoms.
Question: How many atoms are there in each molecule of common salt?

31. How often should I take my medicine? The prescription written by a doctor uses a short-hand that derives from Latin to let you know how to take the medicine being prescribed. Here are some of the terms the doctor uses:
Abbreviation
Latin in full
Meaning
alt. dieb.
alternus diebus
every other day
alt. hor.
alternis horis
every other hour
m. et n.
mane et nocte
morning and night
omn. hor.
omni hora
every hour
Q.h.
quaque hora
every hour
t.i.d.
ter in die
three times daily

Question: What is the meaning of Q.2h. ?

References:
Macmillan Dictionary of Measurement; published 1994
Sizes by John Lord; published 1994 by HarperCollins

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Answers:
1. Five (5) miles square is larger than five (5) square miles;
2. The answer to this odd, not very useful question, is 4;
3. A nanometer is smaller than a millimeter;
4. A crotchet is a quarter note;
5. No;
6. You'll have to find this out for yourself.
7. 55 yards per hour is slower than 5 yards per minute;
8. The Beaufort scale;
9. In a thunder and lightning storm you see the lightning before you hear the rumble of the thunder unless the storm is right overhead. If you can count 5 seconds between the lightning and the thunder you will know that the storm is about a mile away. Sound can be measured in Decibels;
10. Light travels faster than sound. A thunder and lightning storm demonstrates this;
11. There are 1440 minutes in one 24 hour day;
12. Every four years is a Leap Year with one extra day in February;
13. 155 million years;
14. 120 days;
15. 2 parts in 24 which = 1/12 or one-twelfth
16. 14 to 21 days;
17. 8.9;
18. 2 1/2 (two and a half);
19. 20 (twenty);
20. No, fewer. About 4 mill. per cu. ml.;
21. 10 (ten);
22. The US trillion is one thousand thousand million (12 zeros) but is not commonly used except in popular media. In the UK the word trillion is rarely used and its size when used would be open to careful scrutiny!
23. No, neither. But the metric ton is closer in weight to the UK long ton; it weighs 2,204 lbs 10.144 ounces;
24. Bigger. One liter/litre is the equivalent of 2.1134 US pints and 1.76 UK pints;
25. 8;
26. A distance corresponding to one minute of longitude at the equator. This distance is the same as the UK nautical mile which is 6,082.66 feet or approx, 2,028 yards;
27. UK;
28. About 1,400;
29. Energy and frequency;
30. Two (2); one sodium atom and one chlorine atom (NaCl);
31. Every two (2) hours.


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