T5B: Unit conversions and decibels · Technician Exam Practice

T5B Unit conversions and decibels

Math for electronics: conversion of electrical units, decibels

Radio work constantly mixes small and large numbers, so you need to convert between metric prefixes quickly and understand decibels, the unit used to compare power levels. This group is pure arithmetic with a few patterns to memorize.

Metric prefixes

Each prefix is a power of ten. Moving down to a smaller unit makes the number bigger; moving up makes it smaller.

Prefix	Symbol	Meaning
giga	G	1,000,000,000 (one billion)
mega	M	1,000,000 (one million)
kilo	k	1000 (one thousand)
milli	m	0.001 (one-thousandth)
micro	µ (often typed u)	0.000001 (one-millionth)
nano	n	0.000000001 (one-billionth)
pico	p	0.000000000001 (one-trillionth)

Examples of the method:

Amperes to milliamperes: multiply by 1000. 1.5 A = 1500 mA. Going back, 3000 mA = 3 A.
Watts and milliwatts: 500 mW = 0.5 W.
Volts: one kilovolt is 1000 volts; one microvolt is one-millionth of a volt.

Frequency conversions

Hertz, kilohertz, megahertz and gigahertz each differ by a factor of 1000.

1,500,000 Hz = 1500 kHz = 1.5 MHz
3.525 MHz = 3525 kHz (multiply by 1000 to get the smaller unit)
28,400 kHz = 28.400 MHz (divide by 1000)
2425 MHz = 2.425 GHz

Capacitance: 1 microfarad = 1,000,000 picofarads, so 1,000,000 pF = 1 uF.

Decibels

A decibel (dB) expresses a power ratio on a logarithmic scale: dB = 10 x log10(P2 / P1). You do not need a calculator if you remember a few anchors:

Power doubles: +3 dB (5 W to 10 W)
Power halves: -3 dB
Power times ten: +10 dB (20 W to 200 W)
Power divided by ten: -10 dB

Combine them. A drop from 12 W to 3 W is two halvings, so -3 dB plus -3 dB = -6 dB. Positive means gain or increase; negative means loss or decrease. A 4 times ratio is 6 dB, since 3 + 3.

Key facts to memorize

kilo = 1000; mega = 1,000,000; milli = 1/1000; micro = 1/1,000,000
1 A = 1000 mA; 1 MHz = 1000 kHz; 1 GHz = 1000 MHz
1 uF = 1,000,000 pF
Doubling power = +3 dB; halving = -3 dB
Ten times power = +10 dB
Quadrupling = +6 dB; quartering = -6 dB

Memory hooks

Each step in the prefix ladder is three decimal places.
“Double is three, ten is ten”: the two decibel anchors.

Questions in this group (13): answers shown

T5B01

How many milliamperes is 1.5 amperes?
- A. 0.0000015 milliamperes
- B. 0.0015 milliamperes
- C. 1500 milliamperes ✓ Correct answer
- D. 1,500,000 milliamperes
One ampere is 1000 milliamperes, so 1.5 A x 1000 = 1500 mA. Moving from the base unit to milli means the number gets bigger by 1000.
T5B02

Which is equal to 1,500,000 hertz?
- A. 1500 kHz ✓ Correct answer
- B. 1500 MHz
- C. 15 GHz
- D. 150 kHz
1,500,000 Hz divided by 1000 = 1500 kHz. It is also 1.5 MHz, but 1500 MHz would be a thousand times too large.
T5B03

Which is equal to one kilovolt?
- A. One one-thousandth of a volt
- B. One hundred volts
- C. One thousand volts ✓ Correct answer
- D. One million volts
The prefix kilo means one thousand, so one kilovolt is 1000 volts. One one-thousandth of a volt would be a millivolt.
T5B04

Which is equal to one microvolt?
- A. One one-millionth of a volt ✓ Correct answer
- B. One million volts
- C. One thousand kilovolts
- D. One one-thousandth of a volt
The prefix micro means one-millionth, so one microvolt is 0.000001 volt. One million volts would be a megavolt.
T5B05

Which is equal to 500 milliwatts?
- A. 5 watts
- B. 0.5 watts ✓ Correct answer
- C. 500,000 watts
- D. 500,000,000 watts
Milli means one-thousandth, so 500 mW / 1000 = 0.5 W. Half a watt is 500 milliwatts.
T5B06

Which is equal to 3000 milliamperes?
- A. 0.003 amperes
- B. 0.3 amperes
- C. 3,000,000 amperes
- D. 3 amperes ✓ Correct answer
3000 mA / 1000 = 3 A. Dividing by 1000 converts milliamperes to amperes.
T5B07

Which is equal to 3.525 MHz?
- A. 0.003525 kHz
- B. 35.25 kHz
- C. 3525 kHz ✓ Correct answer
- D. 3,525,000 kHz
1 MHz = 1000 kHz, so 3.525 MHz x 1000 = 3525 kHz. Multiplying by 1000 moves you from megahertz to the smaller kilohertz unit.
T5B08

Which is equal to 1,000,000 picofarads?
- A. 0.001 microfarads
- B. 1 microfarad ✓ Correct answer
- C. 1000 microfarads
- D. 1,000,000,000 microfarads
1 microfarad = 1,000,000 picofarads, so 1,000,000 pF / 1,000,000 = 1 uF. A picofarad is one-millionth of a microfarad.
T5B09

Which decibel value most closely represents a power increase from 5 watts to 10 watts?
- A. 2 dB
- B. 3 dB ✓ Correct answer
- C. 5 dB
- D. 10 dB
Doubling power is a ratio of 2, and dB = 10 x log10(10/5) = 10 x log10(2) = about 3 dB. Doubling power is always +3 dB regardless of the starting level.
T5B10

Which decibel value most closely represents a power decrease from 12 watts to 3 watts?
- A. -1 dB
- B. -3 dB
- C. -6 dB ✓ Correct answer
- D. -9 dB
The ratio is 3/12 = 1/4, and dB = 10 x log10(0.25) = about -6 dB. Halving power is -3 dB, and 12 W to 6 W to 3 W is two halvings, so -3 -3 = -6 dB.
T5B11

Which decibel value represents a power increase from 20 watts to 200 watts?
- A. 10 dB ✓ Correct answer
- B. 12 dB
- C. 18 dB
- D. 28 dB
The ratio is 200/20 = 10, and dB = 10 x log10(10) = 10 x 1 = 10 dB. Every tenfold power increase is +10 dB.
T5B12

Which is equal to 28400 kHz?
- A. 28.400 kHz
- B. 2.800 MHz
- C. 284.00 MHz
- D. 28.400 MHz ✓ Correct answer
1000 kHz = 1 MHz, so 28,400 kHz / 1000 = 28.400 MHz. That is in the 10-meter band.
T5B13

Which is equal to 2425 MHz?
- A. 0.002425 GHz
- B. 24.25 GHz
- C. 2.425 GHz ✓ Correct answer
- D. 242.5 GHz
1000 MHz = 1 GHz, so 2425 MHz / 1000 = 2.425 GHz. Dividing by 1000 moves to the next larger unit.