In which form do we express very large or small numbers, focusing on the base of 10?

The concept of expressing very large or small numbers in terms of the base of 10 is fundamentally rooted in scientific notation. Scientific notation involves writing a number as a product of a coefficient and 10 raised to an exponent. This format makes it easier to work with extreme values, whether they are significantly large or minuscule, as the exponent clearly indicates the scale of the number.

For instance, the number 5,000,000 can be efficiently expressed as (5 \times 10^6) in scientific notation. Similarly, a small number like 0.00042 can be represented as (4.2 \times 10^{-4}). This method not only simplifies calculations but also enhances readability, eliminating the clutter of numerous zeros that can accompany very large or small figures.

Understanding the significance of scientific notation is vital in various fields, especially in engineering and physical sciences, where dealing with a wide range of magnitudes is commonplace. While other forms like decimal form, standard form, and engineering notation exist, they do not universally apply the base of 10 in the same systematic way that scientific notation does. Therefore, expressing numbers using scientific notation is the preferred approach for clarity and efficiency when handling very large or small quantities.