Scientific notation is a way to express very large or very small numbers using powers of 10. A number in scientific notation has the form a × 10ⁿ, where a is between 1 and 10 and n is an integer. For example, 45,000 becomes 4.5 × 10⁴.

Converting between standard and scientific notation is a key skill. To convert a large number, move the decimal point left until you have a single digit before the decimal, and count the moves to find the exponent. For small numbers, move right and use a negative exponent.

Scientific notation makes calculations with very large numbers manageable. The speed of light is about 3 × 10⁸ meters per second. The distance to the nearest star is about 4 × 10¹⁶ meters. Without scientific notation, these numbers would be unwieldy to work with.

Operations with scientific notation follow specific rules. When multiplying, multiply the coefficients and add the exponents. When dividing, divide the coefficients and subtract the exponents. These rules make complex calculations straightforward.