Scientific notation is a compact way to write very large or very small numbers as a single digit (and decimals) times a power of ten.
Converting to and from
To convert to scientific notation, move the decimal point until one non-zero digit remains on the left, and count the moves. 186,000 becomes 1.86 × 10⁵ (decimal moved 5 places left). 0.00042 becomes 4.2 × 10⁻⁴ (moved 4 places right, so the exponent is negative). To convert back, a positive exponent moves the decimal right (bigger number); a negative exponent moves it left.
Doing math with it
- Multiplying — multiply the front numbers and add the exponents. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷.
- Dividing — divide the front numbers and subtract the exponents. (8 × 10⁵) ÷ (2 × 10²) = 4 × 10³.
This is why scientists use it — it turns unwieldy arithmetic with zeros into simple operations on small numbers and exponents.
Frequently asked questions
What is scientific notation? Writing a number as a value between 1 and 10 times a power of ten.
What does a negative exponent mean? A number smaller than 1 — the decimal moves left.
How do I multiply in scientific notation? Multiply the coefficients and add the exponents.