### Converting Metric Units, A Ham Radio Exam Study Page

Several of the exam questions involve converting metric units from one form to another.  By memorizing what a few unit prefixes mean, these questions become easy.  Look at the table below:

 Prefix Size Multiply/Divide by pico one millionth of a millionth .0000000000001 or 1E-12 micro one millionth .000001 milli one thousandth .001 kilo one thousand 1000 mega one million 1,000,000 giga one billion 1,000,000,000

• a kilohertz is one thousand hertz
• a megahertz is one million hertz
• a milliampere is one one thousandth of an ampere
• a microvolt is one one millionth of a volt
 From To Multiply/Divide By Mega Kilo x1000 Kilo Mega /1000 One milli x1000 milli One /1000 milli micro x1000 One micro /1,000,000 pico micro /1,000,000 mega One x1,000,000

The prefix in front of a unit just tells you how many of those units your talking about.  A few examples:

To convert between prefixes, there are two steps you can follow.  First, convert the original unit to single units, (megahertz to hertz for example), then convert the single units to the second prefix, (hertz to kilohertz for example).  To convert from a bigger unit, (megahertz for example), to a smaller unit, (hertz), multiply the number of the bigger units by the number in the right hand column above for the prefix, so 3.525 megahertz, (MHz), is 3.525 x 1,000,000 = 3,525,000 Hertz, (Hz).  To convert from a smaller unit to a larger unit, divide by the number in the right hand column, so 3,525,000 hertz / 1000 = 3525 kilohertz.

Rules of Thumb
Sometimes it’s simpler to remember a few rules of thumb in the next table.  These will become more familiar to you the more you use them for actual radio operations.

Exam Questions:
186|T|5|B|01|C|How many milliamperes is 1.5 amperes?
A. 15 milliamperes
B. 150 milliamperes
C. 1,500 milliamperes
D. 15,000 milliamperes

187|T|5|B|02|A|What is another way to specify a radio signal frequency of 1,500,000 hertz?
A. 1500 kHz
B. 1500 MHz
C. 15 GHz
D. 150 kHz

188|T|5|B|03|C|How many volts are equal to one kilovolt?
A. One one-thousandth of a volt
B. One hundred volts
C. One thousand volts
D. One million volts

189|T|5|B|04|A|How many volts are equal to one microvolt?
A. One one-millionth of a volt
B. One million volts
C. One thousand kilovolts
D. One one-thousandth of a volt

190|T|5|B|05|B|Which of the following is equivalent to 500 milliwatts?
A. 0.02 watts
B. 0.5 watts
C. 5 watts
D. 50 watts

191|T|5|B|06|C|If an ammeter calibrated in amperes is used to measure a 3000-milliampere current, what reading would it show?
A. 0.003 amperes
B. 0.3 amperes
C. 3 amperes
D. 3,000,000 amperes

192|T|5|B|07|C|If a frequency readout calibrated in megahertz shows a reading of 3.525 MHz, what would it show if it were calibrated in kilohertz?
A. 0.003525 kHz
B. 35.25 kHz
C. 3525 kHz
D. 3,525,000 kHz

### Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

### The Valentine's Day Magnetic Monopole

There's an assymetry to the form of the two Maxwell's equations shown in picture 1.  While the divergence of the electric field is proportional to the electric charge density at a given point, the divergence of the magnetic field is equal to zero.  This is typically explained in the following way.  While we know that electrons, the fundamental electric charge carriers exist, evidence seems to indicate that magnetic monopoles, the particles that would carry magnetic 'charge', either don't exist, or, the energies required to create them are so high that they are exceedingly rare.  That doesn't stop us from looking for them though!

Keeping with the theme of Fairbank[1] and his academic progeny over the semester break, today's post is about the discovery of a magnetic monopole candidate event by one of the Fairbank's graduate students, Blas Cabrera[2].  Cabrera was utilizing a loop type of magnetic monopole detector.  Its operation is in concept very simpl…

### Unschooling Math Jams: Squaring Numbers in their own Base

Some of the most fun I have working on math with seven year-old No. 1 is discovering new things about math myself.  Last week, we discovered that square of any number in its own base is 100!  Pretty cool!  As usual we figured it out by talking rather than by writing things down, and as usual it was sheer happenstance that we figured it out at all.  Here’s how it went.

I've really been looking forward to working through multiplication ala binary numbers with seven year-old No. 1.  She kind of beat me to the punch though: in the last few weeks she's been learning her multiplication tables in base 10 on her own.  This became apparent when five year-old No. 2 decided he wanted to do some 'schoolwork' a few days back.

"I can sing that song... about the letters? all by myself now!"  2 meant the alphabet song.  His attitude towards academics is the ultimate in not retaining unnecessary facts, not even the name of the song :)

After 2 had worked his way through the so…