Prefixes, Practical Units and Unit Conversion

Transcript

0:00Introduction

Hello everyone! So, one small puzzle before we start. Your car's speedometer shows seventy two. Your physics problem says twenty. Which speed is bigger? Seventy two, obviously, right? But wait. That seventy two is in kilometre per hour, and the twenty is in metre per second. Today you will see they are exactly equal. And look, units are where JEE students lose the easiest marks: one wrong power of ten, and the whole answer is gone. So, prefixes, practical units and unit conversion. Let's begin!

0:36SI prefixes: a name for each power of ten

So, first the prefixes. Instead of long strings of zeros, each power of ten gets a name. Kilo is ten to the power three, mega six, giga nine, then tera twelve, peta fifteen, and exa eighteen. The letter in brackets is the symbol: small k for kilo, capital M for mega, capital G for giga, and so on. Notice the pattern in the powers? Yes, steps of three! Now the small side, going down. Milli, small m, is ten to the power minus three. Micro, written with the Greek letter mu, is minus six. And nano is minus nine. Then pico, minus twelve, femto, minus fifteen, and atto, minus eighteen. Again steps of three, okay? Two prefixes in this list break the pattern: centi, ten to the power minus two, and deci, ten to the power minus one. Centi you know from the centimetre, right? Now tell me. Capital M and small m: are they the same prefix? Not at all! Capital M is mega, ten to the power six. Small m is milli, ten to the power minus three. That is a factor of ten to the power nine between them! So capital and small letters really matter. Got it?

1:58Rules for writing units

Alright, now the rules for writing units. Rule one: unit symbols are never plural. Ten kilogram is written ten k g, never k g s, okay? No full stop after the symbol, and a space between the number and the unit. Simple, right? Rule two: for a unit named after a person, the symbol is capital but the name is small. So newton is capital N, and pascal is capital P with a small a after it. But the word newton is written with a small n, clear? Rule three: a prefix sticks to its symbol with no space, like kilometre, microsecond, gigahertz. And never two prefixes together. Milli micro second? Wrong! Milli times micro is ten to the power minus nine, that is nano. So write n s, nanosecond. Last rule, and a real trap. Newton metre and millinewton both use one capital N and one small m. So are they the same? No, no! In a compound unit, keep a space or a dot between the symbols: N space m is newton metre. But m N joined together is millinewton, milli as a prefix on newton. One small space changes everything, right?

3:14Practical units you must know

Now, practical units you must know. Tiny lengths: one micron, written mu m, is ten to the power minus six metre. One angstrom, the capital A with a small circle on top, is ten to the power minus ten metre. And one fermi, written f m, is ten to the power minus fifteen metre. Huge lengths: one astronomical unit, A U on screen, is about one point four nine six into ten to the power eleven metre. One light year, l y, is about nine point four six into ten to the power fifteen metre. And one parsec, p c, is about three point zero eight into ten to the power sixteen metre. These numbers are huge, aren't they? Energy: one electron volt is one point six into ten to the power minus nineteen joule. One kilowatt hour is three point six into ten to the power six joule. One calorie, about four point one eight joule. And mass: one tonne is a thousand kilogram, one quintal a hundred kilogram, and one atomic mass unit, small u, is about one point six six into ten to the power minus twenty seven kilogram. Do keep the tonne in mind.

4:31JEE trap: what does the unit really measure?

Now, quick question. Light year. It has the word year in it. So it is a unit of time, right? No, no! This is the trap. One light year is the distance light travels in one year: speed of light into time. So it is a distance. And the parsec is a distance too, okay? Same with the kilowatt hour: kilowatt is power, but kilowatt hour is power into time, so it is energy. And the electron volt has volt in its name, but it is energy, not potential. Don't let the names fool you, got it?

5:06Topper's trick: chain conversion

Now, the topper's trick for any conversion. Suppose I multiply a length by one thousand metre over one kilometre. Is that allowed? Why? Yes, because top and bottom are the same length, so the fraction is just one! Same for one hour over three thousand six hundred second. Multiplying by one changes only the units, never the quantity. Clear? So, one kilometre per hour. Kilometre cancels kilometre, hour cancels hour, and we are left with one thousand metre over three thousand six hundred second: five by eighteen metre per second. Very useful, so remember it.

5:46Example 1: 72 km/h to m/s and g/cm3 to kg/m3

Now, remember our puzzle? Let's finish it. Express seventy two kilometre per hour in metre per second, and five gram per centimetre cube in kilogram per metre cube. Pause the video, and try it first. Done? Okay, let's check. Seventy two into five by eighteen. Seventy two by eighteen is four, four into five is twenty. Twenty metre per second! There you go, puzzle solved: seventy two kilometre per hour and twenty metre per second are the same speed. Now density. One gram is ten to the power minus three kilogram, easy. And one centimetre is ten to the power minus two metre, so one centimetre cube is ten to the power minus two metre cube, right? No, no, careful! This is the JEE trap. The centimetre is cubed, so the ten to the power minus two gets cubed too. One centimetre cube is ten to the power minus six metre cube. So one gram per centimetre cube is ten to the power minus three kilogram, over ten to the power minus six metre cube. That is ten to the power three: a thousand kilogram per metre cube. And five gram per centimetre cube? Five thousand kilogram per metre cube. That's it, done!

7:07Example 2: nuclear density in tonne per cubic centimetre

Now a harder one, JEE level. The density of nuclear matter is about two point three into ten to the power seventeen kilogram per metre cube. Express it in tonne per centimetre cube. Pause and try. Hint: change the kilogram and the metre cube one at a time. Done? Okay, let's check. One tonne is a thousand kilogram, so one kilogram is ten to the power minus three tonne, the small t on screen. And one metre is a hundred centimetre, so one metre cube is a hundred cubed: ten to the power six centimetre cube. Don't forget to cube it! Now, the metre cube sits in the denominator. So do we multiply by ten to the power six, or divide? Divide, exactly! The ten to the power six centimetre cube goes in the denominator. So, two point three into ten to the power seventeen, times ten to the power minus three tonne, over ten to the power six centimetre cube, okay? Just the powers. Seventeen minus three is fourteen, and fourteen minus six is eight. Two point three into ten to the power eight tonne per centimetre cube! That is twenty three crore tonnes in one cubic centimetre, about a thimbleful. Wow, imagine lifting that!

8:28Quick revision: prefixes, practical units, chain conversion

So, quick revision. Prefixes are powers of ten, mostly in steps of three, and capital M is mega while small m is milli. Light year and parsec are distances; kilowatt hour and electron volt are energy. And to convert, multiply by fractions equal to one, and cube the factor for volumes. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!