Math and Unit Conversion Skills

# Math and Calculations Skill Use this skill for any task that involves numeric reasoning or calculations, from simple arithmetic to basic statistics and finance. ## General Principles 1. **Always show your work**: - Write the formulas you are using. - Substitute the actual numbers. - Show intermediate steps, then the final result. 2. **Be explicit about units**: - Carry units through each step. - If units are missing or inconsistent, call that out. 3. **Keep precision reasonable**: - Avoid unnecessary rounding early in the calculation. - Round only at the end, and state the rounding rule (e.g. 2 decimal places). 4. **Sanity-check results**: - Check signs, magnitudes, and whether the answer is plausible. ## Common Tasks and Patterns ### 1. Basic Arithmetic Handle addition, subtraction, multiplication, division, powers, and roots. **Pattern**: 1. Write the expression in a clear mathematical form. 2. Evaluate step by step. 3. Simplify and present the final...

# Unit Conversion Skill Use this skill whenever you need to convert values between units while preserving precision and clearly showing assumptions. ## Supported Unit Families You can convert within (but not across) these families: - **Length**: mm, cm, m, km, in, ft, yd, mi - **Area**: mm², cm², m², km², in², ft², yd² - **Volume**: mL, L, tsp, tbsp, fl_oz, cup, pt, qt, gal - **Mass/Weight**: mg, g, kg, oz, lb, tonne - **Temperature**: °C, °F, K - **Time**: ms, s, min, h, day, week, month (30d), year (365d) - **Speed/Velocity**: m/s, km/h, mph, ft/s, kn - **Currency**: Only when an explicit exchange rate or mapping is provided in the context. If a requested conversion mixes incompatible units (for example, meters to kilograms), explicitly state that it is invalid. ## General Workflow 1. **Identify the source and target units** from the user request. Normalize aliases (e.g. "meters" → "m", "kilometers per hour" → "km/h"). 2. **Determine the unit family** (length, mass, etc.). Rej...