Scientific Notation: The Idea

We write very big or very small numbers as a × 10^n, where 1 ≤ a < 10 and n is an integer. Example: Earth’s mass ≈ 5.97 × 10^24 kg; a grain of sand might be 4.0 × 10^-4 g.

How to convert

1. Move the decimal so the number is between 1 and 10.
2. Count how many places you moved: that’s n.
3. Left move → n positive. Right move → n negative.

Try it

Physics connection

In physics you’ll frequently compare orders of magnitude. For instance, the speed of light is 3.00 × 10^8 m/s while a runner might sprint at 1.0 × 10^1 m/s. The difference in exponents tells you which is larger by powers of ten.