Why are numbers used in chemistry often expressed in scientific notation?
They otten are very large or very small. Printing those types of numbers is onerous.
In chemistry, numbers are often very large or very small due to the different magnitudes of quantities involved, such as atomic masses, molecular weights, or Avogadro's number. Expressing these numbers in scientific notation makes it more convenient to work with them and prevents excessively long or short numbers.
Scientific notation is a way of writing numbers using powers of ten. It consists of two parts: a coefficient and an exponent. The coefficient is typically a number between 1 and 10 (inclusive), and the exponent indicates the power of ten by which the coefficient is multiplied.
For large numbers, scientific notation condenses them by representing the coefficient as a number between 1 and 10, while the exponent indicates how many times the power of ten must be multiplied. For example, instead of writing the speed of light as 299,792,458 meters per second, it can be expressed as 2.99792 x 10^8 m/s.
Similarly, for small numbers, scientific notation allows for compact representation. Instead of writing extremely small numbers with many leading zeros, the coefficient can be expressed as a decimal between 0 and 1, and the exponent represents the negative power of ten. For example, the mass of an electron can be expressed in scientific notation as 9.10938356 x 10^-31 kilograms.
Using scientific notation has several advantages in chemistry. It simplifies the representation of large and small numbers, making calculations and comparisons easier. It also allows scientists to clearly express the accuracy of a measurement by adjusting the number of significant figures in the coefficient. Additionally, when performing calculations with numbers in scientific notation, it is straightforward to manipulate the exponents and perform operations like multiplication, division, addition, or subtraction.