By Michelle Friesen | Updated Aug 30, 2022

Very large and very small numbers written in standard form can be unwieldy, difficult to read, and hard to use in calculations. Converting them to scientific or engineering notation makes them easier to manage and understand.

Why Convert to a Different Notation?

Numbers such as 0.000000003 contain many leading zeros, while values like 34,284,000,000 are cumbersome in raw form. Using a compact notation clarifies magnitude and simplifies mathematical operations.

Scientific Notation Explained

Scientific notation expresses a number as a coefficient between 1 and 10 (not including 10) multiplied by a power of ten. A negative exponent indicates a value smaller than one; a positive exponent indicates a large value. For example:

• 34,284,000,000 → 3.4284 × 10¹⁰
• 0.000000003 → 3.0 × 10^-9

Engineering Notation Explained

Engineering notation converts numbers into a coefficient between 1 and 1,000, using powers of ten in increments of three. This aligns with metric prefixes (kilo‑, mega‑, giga‑, etc.). For example:

• 34,284,000,000 → 34.284 × 10⁹
• 0.0003 → 300 × 10^-6

Key Differences Between Scientific and Engineering Notation

Both notations simplify large and small values, but engineering notation is tailored to the metric system. Its exponents jump by 3 (10³, 10⁶, 10⁹, etc.), matching the thousand‑based scaling of prefixes. Scientific notation, in contrast, uses any integer exponent, offering greater flexibility for precise scientific calculations.

When to Use Which Notation?

Use scientific notation for pure scientific work where exact precision matters. Opt for engineering notation in engineering, physics, and applied sciences where metric prefixes and readability are paramount.