Problem 128 - College Algebra Essentials

Question

How do you know if a number is written in scientific notation?

Step-by-Step Solution

Answer

A number is in scientific notation if it is written in the form \(a \times 10^{n}\) or \(aE^n\), where \(1 \leq a <10\) and \(n\) is an integer. The number part must be between 1 and 10, including 1, and the exponent part is a power of ten.

Step 1: Understanding Scientific Notation

Scientific notation is a way of expressing very large or very small numbers that are difficult to manage in their normal form. A number is in scientific notation if it is expressed as the product of a number between 1 and 10 (including 1) and a power of 10.

Step 2: Identify the Components

To verify, start by looking for two parts - a real number part and an exponent part. The real number part is a number that is at least 1 but less than 10, and it can be a decimal. The exponent part follows 'E' or 'e' or 'x 10' depending upon the representation used and it is a power of 10.

Step 3: Check the Format

Lastly, confirm if the given number complies with the format of scientific notation - A number in the form \(a \times 10^{n}\) or \(aE^n\), where \(1 \leq a <10\) and \(n\) is an integer. If it fits this format, it is indeed a number expressed in scientific notation.