Scientific notation
01 // Why labs use it
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of 10, like 6.02 × 10²³ instead of 602,000,000,000,000,000,000,000. Lab science regularly deals with numbers at extreme scales — the mass of an atom, the number of molecules in a sample, the wavelength of light — and writing all those zeros by hand invites mistakes.
The exponent tells you which direction and how far to move the decimal point: a positive exponent means a large number, a negative exponent means a small number between 0 and 1.
02 // Worked example
A student measures a sample's mass as 0.000456 grams on a sensitive balance and wants to write it in scientific notation.
| Measured mass | 0.000456 g |
Formula move the decimal point until one nonzero digit remains in front of it, count the moves as the exponent
03 // Common mistakes
- The coefficient must be between 1 and 10 — a value like 45.6 × 10⁻⁵ is mathematically equal but not correctly formatted scientific notation.
- Moving the decimal point to the right (making the number look smaller in front) gives a negative exponent, and moving it left gives a positive exponent — it's easy to flip the sign by accident.
- Keep the same number of significant figures from the original measurement when converting — scientific notation changes how a number looks, not how precise it is.
04 // Questions people ask
How do you convert a number to scientific notation?
Move the decimal point until only one nonzero digit remains to its left, then count how many places you moved it — that count becomes the exponent. Moving the decimal left gives a positive exponent (large numbers); moving it right gives a negative exponent (small numbers).
Why do labs use scientific notation instead of writing out the full number?
Lab measurements often involve extremely large or small quantities, like the number of atoms in a sample or the mass of a single cell. Scientific notation keeps these numbers short and far less prone to miscounting zeros by hand.
Does scientific notation change how precise a measurement is?
No — converting a number to scientific notation is just a different way of writing the same value. The number of significant figures in the coefficient should match the precision of the original measurement.