Scientific notation (or standard form) is a method of expressing very large or very small numbers in a more manageable and compact form. This system expresses numbers as a product of two parts: a number (called the coefficient) between 1 and 10, and a power of 10. This notation is especially useful in science and engineering where the values can span many orders of magnitude, either much larger or much smaller than everyday numbers. Using scientific notation simplifies the process of handling such extreme values and ensures clarity in communication, particularly when dealing with measurements of distances, times, masses, or energies that fall outside the usual range of numbers we encounter daily.
The scientific notation is written as:
a×10n
Where:
- a is a coefficient that is greater than or equal to 1 but less than 10.
- n is an integer exponent that represents the power of 10.
Examples:
-
0.00034 = 3.4×10−4
This expresses the small number 0.00034 as a product of 3.4 and a power of 10, making it easier to work with, especially in calculations. -
150,000 = 1.5×105
A large number like 150,000 is simplified into scientific notation as 1.5×105, making it easier to handle in equations or scientific contexts. -
0.0000067 = 6.7×10−6
This expresses 0.0000067 as 6.7×10−6, demonstrating how scientific notation allows us to manage very small numbers efficiently. -
8,200,000 = 8.2×106
Here, 8.2 million is written as 8.2×106, compacting a large number into a more manageable form. -
0.00012 = 1.2×10−4
A small number like 0.00012 is written as 1.2×10−4, which is more convenient for calculations in scientific contexts.
In these examples, the numbers are presented in a standardized format that eliminates the need for zeros and makes it clear how many places the decimal point must move.