Problem 129 - College Algebra Essentials

Question

Explain how to convert from scientific to decimal notation and give an example.

Step-by-Step Solution

Answer

To convert a number from scientific to decimal notation, move the decimal point in the number part the number of places equivalent to the absolute value of the power of 10. Move it to the right if the power is positive, or to the left if it's negative. For instance, \(4.5 × 10^3\) is '4500' in decimal notation.

Step 1: Understanding Scientific Notation

Scientific notation is a way of expressing numbers, particularly very large or very small numbers. The format is \(a × 10^n\), where \(a\) is a number greater than or equal to 1 and less than 10, and \(n\) is an integer.

Step 2: Converting To Decimal Notation

To convert from scientific to decimal notation, move the decimal point in \(a\) to the right if \(n\) is positive or to the left if \(n\) is negative. The number of places you move is equal to the absolute value of \(n\).

Step 3: Example

Let's take an example, \(4.5 × 10^3\). As \(n\) is positive and equivalent to 3, move the decimal point in \(4.5\) three places to the right. If there aren't enough digits after the decimal point, fill in with zeros. Therefore, the result is '4500'