How it works
Scientific notation writes any number as a coefficient between 1 and 10, multiplied by a power of ten — a compact way to handle very large or very small numbers without a string of zeros.
x = a × 10b where 1 ≤ |a| < 10
Worked example
Converting 452,000 to scientific notation.
- Move the decimal point until one non-zero digit remains in front: 4.52.
- Count how many places it moved: 5.
452,000 = 4.52 × 10⁵.
Common questions
What does a negative exponent mean here?
It means the original number was smaller than 1 — 0.00047 becomes 4.7 × 10⁻⁴, since the decimal point moved 4 places to the right to reach 4.7.
Why must the coefficient be between 1 and 10?
That's the normalized form — it makes every number's scientific notation unique. 45.2 × 10⁴ and 4.52 × 10⁵ represent the same value, but only the second is in standard form.
How is this useful for very small numbers?
It avoids writing out long strings of leading zeros — 0.0000000001 is far easier to read and work with as 1 × 10⁻¹⁰.