---
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.