Scientific notation
Some numbers are far too big or too small to read at a glance. How do you write them, compare them and calculate with them without counting zeros?
Where you are 3 inside
What this area is about
The distance to the Sun and the width of a hair both come with long runs of zeros, and the size of such a number hides in how many there are. Scientific notation writes a number as a \times 10^{n}, with 1 \le a < 10 and n an integer. The exponent n carries the size; the leading part a carries the digits that matter.
How these fit together
The form. Writing and reading scientific notation defines the form and moves between it and ordinary notation, for large numbers and for small ones, where the exponent is negative, and reads a calculator display such as \texttt{4.2E-6}.
Using it. Comparing numbers in scientific notation works with positive numbers in this form: the larger exponent gives the larger number, and the leading part only breaks a tie; it also estimates how many times larger one is than the other. Calculating in scientific notation multiplies and divides by combining the leading parts and adding or subtracting the exponents, then adds and subtracts once the powers of ten match.
A path through it
Writing and reading the form comes first, and it leans on powers of ten and zero and negative exponents. Comparing and calculating follow, in either order.
Finish here and very large and very small measurements, the kind found in science texts and on a calculator screen, can be read, ordered and combined without writing out a single long string of zeros.