| --- |
| license: cc0-1.0 |
| language: |
| - en |
| tags: |
| - math |
| - reasoning |
| - unit-conversion |
| - synthetic |
| - chain-of-thought |
| size_categories: |
| - 1K<n<10K |
| task_categories: |
| - text-generation |
| - question-answering |
| --- |
| |
| # Unit Conversion Reasoning |
|
|
| A small, fully synthetic dataset of unit-conversion word problems with step-by-step |
| worked solutions, covering **length, weight, volume, temperature, and time**. |
|
|
| ## Dataset Summary |
|
|
| Each example presents a unit-conversion problem (a direct conversion instruction, |
| a chained multi-step conversion, or a short word problem) along with a |
| step-by-step "reasoning" trace and a final "answer" string. The dataset was |
| generated programmatically from a fixed table of conversion factors (and the |
| standard Celsius/Fahrenheit/Kelvin formulas for temperature) — there is no |
| scraped or human-written content. |
|
|
| - **Total examples:** 1,500 (deduplicated) |
| - **Train / test split:** 90% / 10% (1,350 / 150) |
| - **Categories:** `length`, `weight`, `volume`, `temperature`, `time` |
| - **Difficulties:** `easy` (single-step), `medium` (chained, two-step), `hard` (word-problem phrasing) |
|
|
| ## Schema |
|
|
| | Field | Type | Description | |
| |--------------|--------|--------------------------------------------------------------------------| |
| | `question` | string | The conversion problem, either a direct instruction or a word problem. | |
| | `answer` | string | The final numeric answer with its unit, e.g. `"29.199475 feet"`. | |
| | `reasoning` | string | A step-by-step worked solution explaining the conversion. | |
| | `category` | string | One of `length`, `weight`, `volume`, `temperature`, `time`. | |
| | `difficulty` | string | One of `easy`, `medium`, `hard`. | |
|
|
| ### Example row |
|
|
| ```json |
| { |
| "question": "Convert 8.9 meters to feet.", |
| "answer": "29.199475 feet", |
| "reasoning": "Step 1: 1 meter = 1 meter, and 1 foot = 0.3048 of the same base unit, so 1 meter = 3.28084 feet.\nStep 2: 8.9 meters x 3.28084 = 29.199475 feet.", |
| "category": "length", |
| "difficulty": "easy" |
| } |
| ``` |
|
|
| ## Generation Method |
|
|
| The dataset is produced by `generate_dataset.py`, using fixed, standard conversion |
| factor tables for length, weight, volume, and time (each expressed relative to a |
| base unit — meter, gram, liter, second), and the standard linear/affine formulas |
| for Celsius/Fahrenheit/Kelvin temperature conversion. |
|
|
| For each example, the script: |
| 1. Picks a category and a difficulty level. |
| 2. **Easy** — generates a single direct conversion between two random units in |
| that category. |
| 3. **Medium** — generates a chained conversion through an intermediate unit |
| (e.g. inches → meters → kilometers), requiring two reasoning steps. |
| 4. **Hard** — wraps a single or two-step conversion in a short word-problem |
| template (e.g. "A recipe calls for 2.5 liters of milk, how many cups is that?"). |
| 5. Computes the exact numeric result from the conversion factors directly |
| (not from the displayed reasoning text), formats the question/answer/reasoning |
| strings, and records the category and difficulty. |
|
|
| Problems are deduplicated by exact question text. After deduplication, every |
| row is passed through an independent checker (`validate_row` in the generation |
| script) that re-parses the numeric value out of the `answer` string and confirms |
| it matches the actual computed conversion to within a small numeric tolerance; |
| any row that fails this check is dropped before the dataset is saved. |
|
|
| The dataset is purely synthetic and rule-based: no scraping, no external text |
| sources, and no human annotation were used. |
|
|
| ## Intended Use |
|
|
| This dataset is intended for: |
| - Evaluating LLMs' quantitative reasoning and unit-conversion accuracy. |
| - Fine-tuning or instruction-tuning models to produce step-by-step |
| arithmetic/conversion reasoning. |
| - Benchmarking chain-of-thought consistency (does the reasoning trace actually |
| support the final answer?). |
|
|
| It is **not** intended as a general-purpose math benchmark — it covers a narrow |
| domain (unit conversion) and uses a fixed set of templates and units, so models |
| can in principle overfit to its surface patterns. |
|
|
| ## Limitations |
|
|
| - Templates and unit lists are fixed and limited, so question phrasing has |
| noticeable repetition across the dataset. |
| - Numeric answers are rounded for display (typically to 6 decimal places or |
| fewer); exact-string-match evaluation should allow for reasonable numeric |
| tolerance rather than requiring exact text equality. |
| - Only "everyday" units are covered (no scientific/imperial obscure units like |
| furlongs, slugs, etc.). |
|
|
| ## License |
|
|
| This dataset is released under **CC0 1.0 (Public Domain Dedication)**. It is |
| entirely synthetic, generated from arithmetic conversion formulas, and contains |
| no personal, copyrighted, or scraped data. |
|
|
