Why we use scientific notation

Some numbers in science are enormous — the distance to the Sun is about 150 000 000 km — and some are tiny. Writing all those zeros is slow and easy to get wrong. Scientific notation is a short, tidy way to write them.

The form a × 10ⁿ

A number in scientific notation looks like

a × 10ⁿ,

where the coefficient a is at least 1 and less than 10, and the exponent n is a whole number. The distance to the Sun becomes 1.5 × 10⁸ km — much shorter.

What the exponent tells you

The exponent counts how many places the decimal point sits away from where it would be in the plain number. A large number has a positive exponent; the bigger the exponent, the bigger the number. This makes huge numbers easy to compare at a glance.

Three rules that always help

• The coefficient must be at least 1 and less than 10.
• The exponent is a whole number that records the size.
• Scientific notation keeps long numbers short and easy to compare.

Keep going

• Read next: Converting to and from standard form
• Back to the scientific notation overview