Number Scale Converter

Large and small numbers cause misreading errors. A value like 123456789 is easy to miscount by one order of magnitude, and the cost of that mistake in engineering or finance is real. This tool converts raw numeric values into human-readable scaled representations using the SI (International System of Units), Time (day, hour, minute, second, sub-second), and IEEE 1541 (binary powers of 1024) scales. It supports four rounding modes - ceil, floor, banker's even, and odd - and a recursive decomposition mode that breaks a number into multiple unit tiers (e.g., 1d 10h 17m). You can also define fully custom scales with arbitrary prefixes and base values.

The tool approximates values at the precision you choose. Rounding propagation across recursive tiers uses remainder subtraction, not independent rounding, so cumulative drift stays below 1 unit of the smallest tier. Note: the parser (reverse conversion) expects well-formed strings; ambiguous suffixes like m (milli vs. meter) resolve to the active scale context only.

The converter locates the largest scale tier whose absolute base value does not exceed the input magnitude, then divides:

Where n is the input number, base_tier is the multiplier of the matched scale tier, and p is precision (decimal digits). Rounding modes operate on the shifted value v = n × 10^p:

For recursive decomposition of depth d, the algorithm iterates: extract the integer portion at the current tier, subtract its contribution, descend to the next smaller tier, and repeat up to d + 1 terms. The last term receives the fractional remainder rounded at precision p.

Banker's rounding resolves the half-way case: if the digit immediately after the rounding position is exactly 5 with no further nonzero digits, the value rounds to the nearest even number. Odd rounding mirrors this toward the nearest odd number.