METRIC SYSTEM
The Men"ic System is used in electronics for many of the measurements because no
measurements exist in the English systom. Resistors are measured in ohms, kilohms and megohms;
capacitors in farads, microfarads and picofarads. Oscilloscopes measurc waveforms in secorids,
milliseconds and microseconds and volts and millivolts. Frequency which atso is used by radio
stations is measured in kilohertz or kilocycles, megahertz or megacycies, and gigahertz oi
gigacycles. Tltit pun of the Meric System you will have to learn because you wiil use it. An
assembler will see a prys list with a resistor--5Kfl or 4.5MQ, that is 5 kiiohms or 4.5 megohms-and have to figure out the color code for them. ,'+.|th.oggtr it will be easy to do even withouipaper,
the explanation and understanding the reason behind thE steps will be harder. The reason th-at it will
be harder is because_you may be unfamiliar with the systonand all the units wili be new, now
words. The Met'ic System is a sirnple system; much easier than the English System that you are
used to using.
Tlre Yetric=Sy,stenis gas=v. In the English System you can measure something using yards,
feet and inches. In the Metng System you can measure something using meters, cer,itimeteld and'
miliimeters. In the English System 1 yard = 3 feet = 36 inches ana t fobr = 12 inches.In rhe Metric
System 1 meter=100 centimeters = 1000 millimeters and 1 centi- meter= 10 miliimeters. In the
English,Sfstem liquids are measured in gallons, quarts, ounces, cups, tablespoons and teaspoons.
the Metric f ystem decaliters, liters, decijiters, centiliters and milliliters. In ihe Engiish Sydtem 1/4
of a gallon =_1 qla{ = 32 ounces = 4 cup! 2 pints :256drams = Ig}teaspoons 64
tablespoons. In the Meric System, everything is in LO's 0.1 decaliters = 1 iiter = 10 deciliters = 100
^
Il
:
I
centilite$ = 1000 milliliters.
Which is easier to gse? !9l1nY $te most common problem in both sysrem. We will convsft
28 inches to feet and yards in the English system and will convert 217 millimete$ to cenrimeters
and meters. English:
inches to feet--28 inches + 12 inchesfoot = 2 4/L2 or 2 U3 feet
inches to yard--2S inches * 36 inches/yard = 28/36 or 7 /9 yards Metric:
millimeters to centimeters-2L7 rnm+ 10 mno/cm = 21.7 cm
millimeters to mete$--ZL7 mnir+ 1000 mrr/meter = 0.277 metor
The- Megic System is easier to use. The English System was put together over the centuries
_
and based on fractions one-half and one-third. The Metric System was designed by scientist as an
international standard of measurement and based on decimali. It uses a base"unit f6r each different
type of thing being measured and prefixes for the relative size. Once you learn how to convert from
one prefix to_ another in one base; you have learned them ail. For example, as an electronic worker
yolr need to learn ro converr 2,500 ohms(O) to 2.5 kilohms(Ko). 2,500e + 1,000o1K{2= 2.5
KQ. !}en you have le_qrned this, you will be able to convert from any base to the kilo- size of that
base. For example, 2,500 meter to2.5 kilometers. 2,50A meters + 1000meterlKm = 2.5 Km. Some
might wish to use multiplication to convert meters to kilometers, 2,500 mste$ * .001 Km/meters =
2.5 Km. The result is the same 2,500 meters = 2.5 Km. Another way which is used often is
remembering which way to move the decimal and how far.
To change from a base unit
to kiio' move the decimai point three piaces to the ieft.
2,500.00 dollars to
kiiodoliars_ (move the decimal point 3 palces ieft) 2.50000 and drop the zeroes to the nght of the disit
5-->2.5 K$. Change the folloudng from the base unit to the Kilojunit:
l.)
6,7AA farads to kilofarads
2.)
14,000liters to kiloliters
3.)
250,000 ohms to kiiohms
4.)
500 watts to kilowatts
1,560,000 amps to kiloamps
6.)
30 meters to kilometers
METRIC SYSTEM
To change from kilo- to the base unit you do everything in reverse. To change 2.5 Kilometers
to rneters multiply by 100Q or divide by .001 or move the decimal to the right 3 places:
2.5 Kilometers x 1000 meters/Km = 2,500 meters
2.5 Kilometers + .001 Kmlmeter = 2,500 meters
move the decimai of 2.5 Km. to the right 3 places to 2,500 meters (we drop the decimalpoint
at the end of whole numbers).
Do the foliowing:
7.) 6.7 Kilofarads to farads
8.)
14
9.)
250 kilohms to ohms
10.)
0.5 kilowatts to watts
11.)
1,560 kiloamps to amps
12.)
0.03 kilometers to meters
Kiloliters to iiters
In the meffic system there are several prefixes for units larger than the base units. There are
several prefixes for units smaller than the base units. Also there are as many base units as there are
things to measrue. The base units are meter for lelgth, are for area, liter for voiume or Iiquid
measqfe, gmms for mass ("weight" in the Engiish $ystem is a bit different.), ohms for resistance,
farad for capacitance, henry for inductance, amp for electric current, wafi for power, second for
time(only used for small units of time), hertz f,or frequency of a signal or alternating crurent, volt for
electromotive force, dynes, er€s qnd newtons lor force, joules for energy, gauss foimagnetic field.s,
coulomb for electric charge. In electonic work you do not use ali those base units. Buiyou wiil use
some of them. You could use most of the prefixes although not with the same base unit.-You will
use kilohm andmegohm but not milliohm or microhm or picohm. However, you will use picofarad
and microfarad but not kilofarad and megafarad. Yet each exist as a part of the Metric Syst-em.
Rattrer than give you thee ways of converting from a particular unit to another unit, I am
shgwing.you. the easiest to remember and the faspst !o get tlre answer. It is counting decimal places
and rnoving it right or left. Also it is less confusing than trying to remmber whether to divide or
multiply by particular numbers. For units larger than the base units:
GIGA- MEGA. MYRIA- KILO. HECTO. DECA- BASE UNIT
9 876
s 4
3
2
r
_0_
The numbers that are underiine go with the prefix above them and stand for the number of
decimal places that you would move the decimal point to change frorn the base unit to the prefix unit
or from the prefix unit to the base unit.
Example: Change 350 ohms to hectohms
Hecto- is over the number 2 and is piaced on the left of the "baso unit." You move the d.ecimal
2places to the 1eft, 350 ohms = 3.5 hectohms.
Example: Change 4500 watts to myriawatts
Myna- is over the number 4 and is piaced on the left of the "base unit." You move the decimal
4 places to the ieft, 4,500 watts= 0.45 myriawatts.
Exampie: Change 8,760,000,000 hertz to gigahertz
Giga- is over the number 9 (8 and 7 do not have prefixe s) and is placed to the left of the base
unit. You move the decimal 9 piaces to the left. 8,760,000,000 hertz = 8.76 gtgahertz.
You can use the chart to change the otherway too.
2
METRIC SYSTEM
Example: Change 6.5 Megohms to ohms
number6 (5 does. notiave a prefex) and ohns is a base unit--to
.
rhe rieht
and over the zero. You move the decimal 6 places to ttre righr
6.5
v'r ^ra!M12= v'J'
6Jdii,OOiid." "t"'
Example: Change 45 hectometers to meters
Hecto- is over 2 and meters is the base unit and is to the right of hecto-. you
move the decimal
2 places to the right
45 hectomet"i, = 4500 meters.
14e8-a- is over-the
GIGA. MEGA-
9 876
MYRIA. IilLO- HECTO- DECA- BASE UNIT
5 4
J
2
1
0
Uriog tlre char:r do the following:
13) 1,2.3 meters to decameters14) 345ffi ares ro hecrares
15) 67,000 watrs to myriawatrs
16) 780,000 farads to megafarads
17) 900,000,000 herz to grgahertz
18)
8.1 Megohms to ohnns
19) 0.45 Kilomerers ro merers
20) I Decamps to amps_
21)
1.3 gigaliters ro lirers
Hoy.{o yousuppose you would change 2.0
Yeggtps to Kilohms? There arc rwo wavs. one
way would be to changefromJVlegohms tobase unit.i.6
Megc,hmsll,ob-olooil"r,_JclJi,iie"""
places to the right) and then_change from base unit m kilo-. 7,600,000
ohms = 7,ftffikilohms
(count 3 places to the-left) W?y Two combines the steps.
Notice thar Mega- over the
number 6 ttrat is underiined and Kilo- is over the 3 that is und.erlined. Als;tha;
rlolt to tfre rilnt oi
Mega-. Subtract the numbers that go with the uniis
the decimal
in the direction that the new unit is on the same side as. That is, Mega- is
6
;"t;;e
and
Kilo- is 3. 6-3=3. Kilo- is on the right side of Mega-. The decimai wiil move
right'^
-- -L--_- giga- . ^
8 gigahertz to hectohertz:
is 9 and hecto-
3 places to the
is2,. 9-2=7. hectdis on tt r'.igirr side of eiea_.
The dec.imal poinlmoves 7 piaces to the
g grtn15err" S0;000d0ii;#"ti3;
=
54,000,000 D":1{Tt-t!
Decais
1
and
Myrfi'[?
?-r=3. 1a*a-- is to the lefr
{rnarrams:
of Deca-. The decimai.moves 3 praceslo the
54,00b,d0b;;$r*; = i;,dcitMrr]ufr;i;.
the
chart
above
convert
the
foliowing
units
foom one to the Sther- Remember m tell
9tqg
the
direction the decimal goes find which side the unlt that you arr iooHng
ir on *it:, respect to the
unit of the number you have been given.
2D 4A gigagrams to myriagrams
righr
iefr.
-.
i*
23) 3,300 hectohms to kilohms
24) 0.005 Megawatts ro kilowatts
25) 48,000,000 decahenries to megahenries_
26) 0.0035 Gigaliters to kiloliters
3
METRIC SYSTEM
Now let us look at the other end of the scale to the units smaller than the base unit. Again, the
prefixes are placed so that moving the decimal point will be the same direction as the side thlt the
prefix is on and the numbers u"d-el the prefix with the underline is the number of decimal places that
the decimal point must be moved from the base unit's decimaL position.
BASE
UI'{IT DECI- CENTI- MILLr- MrcRo- NAN0- pICo-
0
I
2
_3_4s67 8_9,1011L2
To change 2.45 meters to centimeters: meters is a base unit and centi- is the prefix from
^
centimeter and is over the number 2. Centi- is to the right of the base unit. Therefore, the decimal
moves 2 piaces to the right. 2.45 meters =245. centimeters (I do not need to write the d"ecimal
point. I did so that some might see that it is where it lands.)
Example: 0.00045 liter to milliliters:
liter is the base unit and milii- is to right and over 3 (4 and 5 do not have names and. are not
underlined; 3 is underlined and goes with milti-). The decimal point rnust be moved 3 places ro the
right.
0.00045 liter = 0.45 milliliters
If we wanted to change it to microliters from 0.45 milliliters, micro- is to the right and over 6
(again^7 ana.9_9p not have names). 6-3=3. The decimal moves 3 more places to the right.
0.45 milliliters = 450 microliters.'
Exampie: change 300,000 picofarads to farads
Farads is the base unit and pico- is the prdix over 12 and is to the right of the base unit.
Therefore, the decimal point will move to the left 12 places. Notice you are changing from picoto the base unit; the base unit is to the left of pico- The rule is move from the-unit wittr
the numbers to the new unit. Moving
the decimal 12 places to the left 300,000 picofarad.s
= 0.0000003 farads
Example: change 6700 nanohenries to microhenries.
Micro- is over 6 and Nano- is over 9. We are going from nano- to nricro- and micro- is on the
left. Therefore, we movo the decimal point 3 places to the left. (9-6=3) 6700 nanohenries = 6.7
microhenries.
Using the chart at the top of this page change the following:
27) 23.4 grams to decigrams
Zq
434 meters to centimeters
29) 0.0078 amps to milliamps
30) 4,500,000,000,000 picowatts to watts
'3I) 56 nanoseconds to seconds
32) 0.00047 microfarads to picofarads
33) 30.7
miliiiiters to microliters
34) 650,000 microns to centimeters
(micron is used instead of micrometer, which is a measuring
instrument)
35) 0.00079 nanohms to deciohms
4
METRIC SYSTEM
What do you do when the units are on opposite sides of the base units? The direction rules for
right and left are srill 6r same. The only diffeience is now you add the numbers underiined under
thb prefixes t9 get the decimal p,ia9eq, Fbr example if you rianted to change iiS a""u eters ro
decimeters. Deca- is over 1 and deci- is over 7.1+1=2. deci is to right ofine base unit and the base
unit is to the right of deca-. The decimal is moved 2 places to the rilht . z.Z5 decamerers =225.
decimeters.
Another example: 4,500,000,000 microhms to kilohms
liigto- is 6; kilo- is 3. 6+3=9. Kilohms is to the left of the base unit and the base unit is to the
left of micro-. The decimal must be move 9 places to the left.
4,500,000,000 microhms = 4.5 kilohms.
GIGA- MEGA- MYRIA. KILO. HECTO. DECA. BASE UI{IT
e 87 6_ s 4
2
1
0
I
BASE UNIT DECI- CENTI. MILLI- MICRO- NANO- PrcO.
1
2 l- 4 s 6 7 8_e 10 11 12
0_
The chart above is made from the two previous ones put togethsr.
Example: 0.0000000078 megawatrs ro nanowarts
I4._gu: is over 6 and Nano- is over 9. 6+9=15. Nano is to the right of Mega-. The decimal
moves 15 places to the right.
0.0000000078 megawatts = 7,800,000 nanowatrs.
GIGA- MEGA. TYRIA- KILO- IIECTO- DECA- BASE DECI. CENTI- MILLI- MCRO- NANO- PiCO-
96432r0
1236912
Using the above chart, do the following:
36) 45.78 hectograms to milligrams
37) 648.00 centiamps to decamps
38) 1 Megohm to microhm
39) 1,000,000,000,000,000 picofarads to kilofarad
40) 70.89 myrialiters to
4I)
centiliters_
1,23A gigahertz to decihertz
4})3Megohms to ohms
43) 0.089 miiligrams to decagrams
44)
0.25 kilograms to decigrams
45) Il.yoy *.otqq 40 hours per week for 52 weeks and were paid at the hourly rare of $6.25,
how many kilobucks did you
A11 units can be abreviated. Km for kilometer. cg. for centigram- mw for milliwatt. The
.
make?_K$
abreviation for micro- is f-[, the Greek letter mu.
pfd means microfarad, pH is for microhenry, and p or pn is for micron--l pn = 0.000001
meters.
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