Lesson 41 Chapter 8: Prefixes Metric Numbers In the Metric System there are standard ways of talking about big and small numbers: "kilo" for a thousand, "mega" for a million, and more... Example: A long rope measures one thousand meters It is easier to say it is 1 kilometre long, and even easier to write it down as 1 km. In that example we used kilo in front of the word meter to make "kilometre". And the abbreviation is "km" (k for kilo and m for meter, put together). Here are some more examples: Example 2: You put your bag on a set of scales and it shows 2,000 grams, we can call that 2 kilograms, or simply 2 kg. Example 3: The doctor wants you to take 5 thousandths of a litre of medicine (a thousandth is one thousand times smaller), he is more likely to say "take 5 millilitres", or write it down as 5mL. "kilo", "mega", "milli" etc. are called "prefixes": Prefix: a word part that can be added to the beginning of another word to create a new word So, using the prefix "milli" in front of "litre" creates a new word "millilitre". 8 Prefixes Page 1
Here we list the prefix for commonly used big and small numbers: Common Big and Small Numbers Name The Number Prefix Symbol trillion 1,000,000,000,000 tera T billion 1,000,000,000 giga G million 1,000,000 mega M thousand 1,000 kilo k hundred 100 hecto h ten 10 deka da unit 1 tenth 0.1 deci d hundredth 0.01 centi c thousandth 0.001 milli m millionth 0.000 001 micro µ billionth 0.000 000 001 nano n trillionth 0.000 000 000 001 pico p Just remember for large values (each one a thousand times bigger): kilo mega giga tera and for small values (each one a thousand times smaller): milli micro nano pico Try To Do Some Yourself! How would you refer to a million liters? How about one billionth of a meter? 8 Prefixes Page 2
Much Bigger and Smaller There are also prefixes for much bigger and smaller numbers: Some Very Big, and Very Small Numbers Name The Number Prefix Symbol Very Big! septillion 1,000,000,000,000,000,000,000,000 yotta Y sextillion 1,000,000,000,000,000,000,000 zetta Z quintillion 1,000,000,000,000,000,000 exa E quadrillion 1,000,000,000,000,000 peta P Very Small! quadrillionth 0.000 000 000 000 001 femto f quintillionth 0.000 000 000 000 000 001 atto a sextillionth 0.000 000 000 000 000 000 001 zepto z septillionth 0.000 000 000 000 000 000 000 001 yocto y Lengths From Very Small to Very Large Our Universe has very small things (like atoms), and very large things (like galaxies). And this is where metric prefixes like milli- and kilo- can be very useful. Example: The distance between London and New York is about 5,580,000 meters. But it is easier to use 5,580 kilometres. Here is an illustration of sizes, from the very small (a Quark) to the very large (the known Universe). The sizes are in meters using metric numbers (just add the word "meter" after them, so you get "millimetre", "terametre", etc: 8 Prefixes Page 3
The numbers (like 10-18 ) use Scientific Notation to show how big the value is. Example: 10 6 is 10 used in a multiplication 6 times, which is a 1 followed by 6 zeros: 1,000,000. It is also called a million. The prefix is mega-, so a megameter is a million meters. Example: 10-9 is a 1 moved nine places the other side of the decimal: 0.000 000 001 It is also called a billionth. The prefix is nano-, so a nanometre is a billionth of a meter. Looking at the illustration you can see that a person is about 1 meter in size, a mountain is about 10 3 (one thousand) meters in size, and the diameter of the Sun is about 10 9 (one billion) meters. Example: We could also say the Sun is about a "gigameter" in size. It's diameter is actually 1.392 10 9 meters, or 1.392 gigameters, or simply 1.392 Gm More Interesting facts: Quarks are very very small Molecules are around the billionths of a meter in size. That is 0.000000001 meters. Some molecules are smaller and some bigger, though. People are a little over a meter tall, Mountains are kilometers in size. The Earth is megameters in size (a megameter is a thousand kilometers, and the Earth's Diameter is actually 12,000 km) A Light Year is about 10 petameters in size (a petameter is 1,000,000,000,000,000 meters, which is a 1 followed by 15 zeros) The Milky Way is about 1 zetameter across (1,000,000,000,000,000,000,000 meters, which is a 1 followed by 21 zeros) The Universe is very very big 8 Prefixes Page 4
Name All Big Numbers We Know As a Power of 10 Thousand 10 3 1,000 Million 10 6 1,000,000 As a Decimal Billion 10 9 1,000,000,000 Trillion 10 12 1,000,000,000,000 Quadrillion 10 15 etc... Quintillion 10 18 Sextillion 10 21 Septillion 10 24 Octillion 10 27 Nonillion 10 30 Decillion 10 33 Undecillion 10 36 Duodecillion 10 39 Tredecillion 10 42 Quattuordecillion 10 45 Quindecillion 10 48 Sexdecillion 10 51 Septemdecillion 10 54 Octodecillion 10 57 Novemdecillion 10 60 Vigintillion 10 63 8 Prefixes Page 5
All Small Numbers We Know Name As a Power of 10 As a Decimal thousandths 10-3 0.001 millionths 10-6 0.000 001 billionths 10-9 0.000 000 001 trillionths 10-12 etc... quadrillionths 10-15 quintillionths 10-18 sextillionths 10-21 septillionths 10-24 octillionths 10-27 nonillionths 10-30 decillionths 10-33 undecillionths 10-36 duodecillionths 10-39 tredecillionths 10-42 quattuordecillionths 10-45 quindecillionths 10-48 sexdecillionths 10-51 septemdecillionths 10-54 octodecillionths 10-57 novemdecillionths 10-60 vigintillionths 10-63 8 Prefixes Page 6
Scientific Notation / Standard Form Scientific Notation (also called Standard Form) is a special way of writing numbers that makes it easier to use big and small numbers. You write the number in two parts: Just the digits (with the decimal point placed after the first digit), followed by 10 to a power that would put the decimal point back where it should be (i.e. it shows how many places to move the decimal point). In this example, 5326.6 is written as 5.3266 10 3, because 5326.6 = 5.3266 1000 = 5326.6 10 3 How to Do it To figure out the power of 10, think "how many places do I move the decimal point?" If the number is 10 or greater, the decimal place has to move to the left, and the power of 10 will be positive. If the number is smaller than 1, then decimal place has to move to the right, so the power of 10 will be negative: Example: 0.0055 would be written as 5.5 10-3 Because 0.0055 = 5.5 0.001 = 5.5 10-3 Check After putting the number in Scientific Notation, just check that: The "digits" part is between 1 and 10 (it can be 1, but never 10) The "power" part shows exactly how many places you moved the decimal point 8 Prefixes Page 7
Why Use It? Because it makes it easier when you are dealing with very big or very small numbers, which are common in Scientific and Engineering work. Example it is easier to write (and read) 1.3 10-9 than 0.0000000013 Example: Suns, Moons and Planets The Sun has a Mass of 2.0 10 30 kg. It would be too hard for scientists to have to write 2,000,000,000,000,000,000,000,000,000,000 kg It can also make calculations easier, as in this example: Example: a tiny space inside a computer chip has been measured to be 0.00000256m wide, 0.00000014m long and 0.000275m high. What is its volume? Let's first convert the three lengths into scientific notation: width: 0.000 002 56m = 2.56 10-6 length: 0.000 000 14m = 1.4 10-7 height: 0.000 275m = 2.75 10-4 Then multiply the digits together (ignoring the 10s): 2.56 1.4 2.75 = 9.856 Last, multiply the 10s: 10-6 10-7 10-4 = 10-17 (this was easy: I just added -6, -4 and -7 together) The result is 9.856 10-17 m 3 Engineering Notation Engineering Notation is like Scientific Notation, except that you only use powers of ten that are multiples of 3 (such as 10 3, 10-3, 10 12 etc). Example: 19,300 would be written as 19.3 10 3 Example: 0.00012 would be written as 120 10-6 Notice that the "digits" part can now be between 1 and 1,000 (it can be 1, but never 1,000). 8 Prefixes Page 8
The advantage is that you can replace the 10s with Metric Numbers. So you can use standard words (such as thousand or million) prefixes (such as kilo, mega) or the symbol (k, M, etc) Example: 19,300 meters would be written as 19.3 10 3 m, or 19.3 km Example: 0.00012 seconds would be written as 120 10-6 s, or 120 microseconds 8 Prefixes Page 9
Prefixes Q1 Write down the name and symbol of the derived unit for: (the first one has been done for you) Derived unit Name Symbol a) one thousand metres kilometres km b) one thousandth of a watt c) one million joules d) one millionth of an ohm one millionth of a e) kilonewton f) one million millivolts Q2 Give the prefix we would put in front of a unit if we wanted to multiply it by the following numbers: (the first one has been done for you) Value Prefix Abb. Value Prefix Abb. a) 10 3 kilo k b) 10 6 c) 10-3 e) 10 9 d) 10-6 f) 0.000 000 000 1 g) 1/10 h) 1/1 000 000 0.000 000 000 i) 001 j) 1 000 000 000 000 Q3 Round the following numbers up or down: a) 3645N to the nearest kn b) 195 seconds to the nearest minute c) 13.27 cm to the nearest mm d) 2493 kw to the nearest MW e) 12.56 Nm to the nearest joule f) 9854399 amps to the nearest kilo amp Q4 Convert the following to the unit given. 8 Prefixes Page 10
a) 1.125 kilowatts to watts b) 25 microcoulombs to coulombs c) 0.0006 microfarad to picofarads d) 3.3 kv to volts e) 0.037 A in milliamperes f) 0.45 M to ohms g) 0.000596 M to ohms h) 49378 W to kilowatts i) 1.68 C to coulombs j) 724 mw to watts Q5. Convert the following resistance values to ohms: a) 3.6 b) 20.6 c) 0.0016M d) 0.68 k e) 0.085 M f) 46500 m Q6 Q7 Q8 Q9 The current in a circuit is 16.5 ma. Change this to amperes. Sections of the Grid system operate at 132 000V. How many kilovolts is this? Add the following resistances together and give the answer in ohms: 18.4, 0.000 12 M, 956 000 The following items of equipment are in use at the same time: four 60 W lamps, two 150 W lamps, a 3 kw immersion heater, and a 1.5 kw radiator. Add them to find total load and give the answer in watts. Q10 The following loads are in use at the same time: a 15 W lamp, a 750 W iron, and a 3.5 kw washing machine. Add them together and give the answer in kilowatts. Q11 Q12 Q13 Add 34250 to 0.56 M and express the answer in ohms. From 25.6 ma subtract 4300 A and give the answer in amperes. The mass of one atomic group of particles is 2.275 10-14 grams. Calculate the total mass of 2000 groups of particles. Give your answer in kg. 8 Prefixes Page 11
Q14 Q15 Q16 Q17 The mass of the moon is 7.343 10 19 tonnes. The Earth has a mass 81 times bigger than of the moon. a) Work out the mass of the Earth, giving your answer in standard form and in kg. b) The mass of a meteorite is 3.61 10 7 kg. Write 3.61 10 7 as an ordinary number. The mass of a neutron is 1.675 10-24 grams. Calculate the total mass of 1500 neutrons. Give your answer in standard form and in kg. The capacity of a computer is 500 megabytes. One megabyte is 10 3 kilobytes. One kilobyte is 1.024 10 3 bytes. Find the capacity of the computer in bytes, giving your answer in standard form. A capacitor is marked 1000 F. a) What is its capacitance in farad? b) What is the charge on it at 20V? Use the formula Q = VC. 8 Prefixes Page 12