T5B: Math for Electronics

Two types of math appear throughout amateur radio: unit conversions and decibel calculations. Neither requires advanced math — unit conversions involve multiplying or dividing by powers of ten, and the decibel questions on the Technician exam involve just a few key reference points worth memorizing. Master these two skills and the T5B questions become straightforward.

This group covers the metric prefix system used in electronics (milli, kilo, micro, mega, giga, pico), how to convert between units using those prefixes, and how to use the decibel scale to express power ratios. Every conversion and decibel question in T5B has a definite correct answer that follows directly from knowing the prefix values and a small set of decibel benchmarks.

The Metric Prefix System

Electronics uses the metric prefix system to handle quantities that range from tiny fractions to enormous numbers. Instead of writing 0.001 amperes, you write 1 milliampere. Instead of writing 1,000,000 hertz, you write 1 megahertz. Each prefix represents a specific power of ten multiplied by the base unit.

Notice that kilo uses a lowercase "k" — this is the correct SI convention, distinguishing it from the uppercase K used for Kelvin (temperature). In amateur radio, the megahertz abbreviation is MHz (capital M, capital H, lowercase z) and kilohertz is kHz (lowercase k, capital H, lowercase z). These exact capitalizations appear in the exam questions.

Unit Conversion Examples

Converting between prefix levels is a matter of moving the decimal point. Going from a larger prefix to a smaller one (e.g., amperes to milliamperes), multiply by 1000. Going from a smaller prefix to a larger one (e.g., milliwatts to watts), divide by 1000.

The most common conversion error is moving the decimal in the wrong direction. A reliable approach: when converting to a smaller unit (e.g., MHz to kHz), the number gets larger (3.525 MHz → 3525 kHz). When converting to a larger unit (e.g., kHz to MHz), the number gets smaller (28400 kHz → 28.400 MHz).

The picofarad-to-microfarad conversion is especially worth memorizing: there are 1,000,000 picofarads in one microfarad (pico is one-millionth of micro, and micro is one-millionth of a base unit, so pico is 10⁻¹² of the base unit). 1,000,000 pF = 1 µF.

Decibels: Expressing Power Ratios

The decibel (dB) is a logarithmic unit used to express ratios between power levels. Because power levels in amateur radio span an enormous range — from microwatts of received signal to hundreds of watts of transmitted power — a logarithmic scale is far more convenient than expressing everything as raw ratios.

A positive dB value means a power increase; a negative dB value means a power decrease. The key benchmarks to memorize are:

These benchmarks are additive on the dB scale. A factor of 4 increase = doubling twice = +3 dB + 3 dB = +6 dB. A factor of 20 increase = ×10 then ×2 = +10 dB + 3 dB = +13 dB. This additivity makes the dB scale extremely useful for calculating gains and losses through a chain of amplifiers and attenuators.

Decibel Calculation Examples

The T5B exam questions ask you to identify the dB value for specific power changes. Working through each one:

The key to each problem is identifying the ratio first, then matching it to the benchmark table. 12÷3 = 4, so this is a factor of 4 decrease = −6 dB. 200÷20 = 10, so this is a factor of 10 increase = +10 dB. Do not try to memorize specific wattage pairs — understand the ratios and apply the benchmarks.

T5B Practice Questions