Decimal Spelling Scale Aligner
Align a list of decimal spellings to a common exact coefficient scale; no precision loss or rounding.
Description
Align a list of decimal spellings to a common exact coefficient scale; no precision loss or rounding.
Aligning decimal scales puts exact values on one common power-of-ten coefficient grid.
When to use this tool
Align a list of decimal spellings to a common exact coefficient scale; no precision loss or rounding.
- Prepare the supplied decimals fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter decimals. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.scale, result.coefficients. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Parse every decimals entry, choose the maximum effective scale and multiply each coefficient by 10^(common scale minus original scale). Return scale and exact coefficient strings.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| decimals | decimals. | List of strings; at most 128 entries |
| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.scale | The scale value under the stated formula or text convention. |
| result.coefficients | The coefficients list in the ordering and representation described above. |
{
"input": {
"decimals": [
"1.2",
"0.003"
]
},
"output": {
"result": {
"scale": 3,
"coefficients": [
"1200",
"3"
]
}
}
}Limitations and assumptions
- Empty input yields scale zero and no coefficients. Original notation and signed-zero spellings are not preserved; aligned coefficients are not floating-point numbers.
- Exact decimal-spelling operations require digits before the optional decimal point and allow a signed exponent. Decimal text is bounded to 256 code units and effective scale to minus 256 through 256; integer-string fields allow a sign and up to 256 digits.
- Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
- Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
- Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.
Alternative or Complementary methods
Preserve decimal and integer strings when exact comparisons matter. Select signedness, scale, rounding and overflow policies separately, and use the matching encoder/decoder rather than a floating-point approximation.
References
Similar or alternative tools
- Decimal Spelling Exact Comparison
Compare finite decimal spellings exactly using BigInt scale alignment, not IEEE-754 conversion.
- Decimal Exponent Spelling Compactor
Compact an exact finite decimal spelling into canonical scientific notation without numeric parsing.