How can you read numbers that are written in scientific notation? Why is scientific notation important?
it saves having to write out a lot of zeros, reducing the chance for error (and writer's cramp)
one digit to the left of the decimal point
... the magnitude expressed as a power of ten
371 = 3.71x10^2 ... or ... 3.71E2
... E describes the exponent of ten
.00263 = 2.63x10^-3 ... or ... 2.63E-3
To read numbers written in scientific notation, you need to understand the two components: the coefficient and the exponent. The coefficient is a number between 1 and 10 (inclusive), and the exponent represents the power of 10.
Here's an example: 3.2 x 10^4
To read this number, first read the coefficient: "3.2". Then, determine the power of 10 by looking at the exponent: "10^4". The exponent of 4 means you need to write four zeros after the coefficient. So, the number "3.2 x 10^4" in scientific notation is equivalent to "32,000" in standard form.
Scientific notation is important because it allows us to express very large or very small numbers in a compact and convenient way. It is commonly used in fields like science, engineering, and astronomy where dealing with extremely large or small values is frequent. Instead of writing out numerous zeros, scientific notation simplifies the representation of these numbers, making calculations and interpretations easier. It also helps in maintaining accuracy and precision when working with measurements or calculations involving very large or small quantities.