A decade resistance box arranges its resolution as a stack of rotary decades, each one contributing a value 10× larger than the dial below it, so a six-dial instrument reaches 0 to 999,990 Ω in 10 Ω steps [S4].
Each dial is a 1-2-3…10 weighted switch, not a linear potentiometer, and the total output is the series sum of every dial's selected position, which is why the box behaves like a mechanical decimal readout [S1][S2].
Why the decades are weighted by 10, not 1-2-5
Each rotary switch in a decade box offers ten positions, with internal resistors stepping 1×, 2×, 3×, … 10× the per-step weight of that decade, which is why a 1-2-5 layout would lose the 4, 6, 7, 8, 9 positions [S1][S3].
Because the decades are organized in powers of ten, the lowest decade defines the box's least significant bit: a six-dial instrument with an LSB of 10 Ω achieves one part-per-million resolution relative to its full-scale 999,990 Ω, and dropping the LSB to 1 Ω or 0.1 Ω pushes resolution further [S6].
Reading the dials like a decimal number
The switches on a decade box are labeled to mirror decimal place value, with one dial for the units (Ω), one for the tens, one for the hundreds, and so on, so a setting of 2-3-4-5 across four dials reads as 2 + 30 + 400 + 5,000 = 5,432 Ω [S2].
The original SparkFun hookup guide makes the same point: a control for the ones position, a control for the tens position, a control for the hundreds position, and so on, and the cumulative reading is the sum of the weighted positions [S3][S4].
Comparison: decade stepping versus other step schemes
Three step schemes are used across substitution-box designs, and the trade-off is coverage versus resolution: [S6]
1-2-2-5 (1, 2, 2, 5 decade steps per dial) is common on inductance and capacitance decades, where matched component values are scarce, so each dial needs fewer precision parts but you lose intermediate codes and need a 4-dial stack to get 0-9,999 in 1 Ω steps.
1-2-3-…10 weighted decades give full decimal coverage with one position per integer from 0 to 9, which is the standard arrangement on resistance decades and is what the 0 to 999,990 Ω, in 10 Ω increments specification assumes [S4].
Binary-stepped boxes (1-2-4-8) cut the parts count per dial to four resistors, which suits precision lab references, but the dial no longer reads like a decimal digit, so a seven-bit dial replaces what a 1-2-3-…10 dial does in fewer switches [S3].
Where the resolution step matters in practice
Bridge and null-measurement work, including Wheatstone bridge balancing, is where the LSB of the lowest decade directly limits how close to the true null the operator can tune the reference, so a 1 Ω LSB buys a tighter balance than a 10 Ω LSB at the same full scale [S5].
For calibration of meters and ohmmeters, the highest decade typically defines the upper bound, while tolerance and the lowest-decade resistor accuracy define the box's overall accuracy class, with high-grade boxes reaching tolerances as low as 0.1 percent [S1].
What the dials will not give you
A decade box is a discrete instrument: every dial snaps to one of its ten positions, so it cannot produce values between the LSB steps, and contact resistance of the rotary switch adds a small but nonzero error that dominates at very low ohm settings [S2].
Traditional units were built in large wooden enclosures with engraved front panels and Bakelite knobs, and the discrete-step architecture is the reason they survived unchanged in physics labs while analog rheostats faded out [S3][S4].
Sourcing and standards
Public manufacturer documentation, including the SparkFun hookup guide and ManualsLib archive, treats the 0 to 999,990 Ω, in 10 Ω increments spec as the canonical demonstration of weighted-decade stepping for kit-built and lab instruments [S3][S4].
Educational references such as Fiveable's College Physics I entry confirm the units-tens-hundreds-thousands labeling convention used on physical decade boxes, and tie the weighted-step layout to null-measurement technique rather than to any single IEC or ISO clause [S5].
For a broader selection view across range, accuracy, and calibration-lab use, the SourceBySpec selection guide covers how resolution, dial count, and LSB choice interact when sizing an instrument for a given job [S6].
For engineers bridging the same idea from resistance to other physical quantities, the single-acting vs double-acting plunger pump selection matrix applies a similar weighted-decade mental model to flow steps, and the 1 kHz vs 100 kHz data logging for transients spec decision guide treats sampling-rate choice as a discrete-step LSB problem on the time axis.
The underlying component specifications are covered under brake resistor, and dial indicator.