Problem 105 - College Algebra

Question

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

Step-by-Step Solution

Answer

To convert from scientific to decimal notation, identify the values of \(a\) and \(n\) in the scientific notation \(a \times 10^n\). Then, if \(n\) is positive, move the decimal point in \(a\) to the right by \(n\) places, and if \(n\) is negative, move the decimal point in \(a\) to the left by \(|n|\) places. For instance, \(3.5 \times 10^3\) in decimal notation is \(3500\).

Step 1: Understand Scientific Notation

Scientific notation is a form of representing very large or very small numbers that are inconvenient to write in decimal form. It is expressed as \(a \times 10^n\), where \(1 \leq |a| < 10\) and \(n\) is an integer.

Step 1: Identify the Values

To convert from scientific to decimal notation, first identify the values of \(a\) and \(n\) in the scientific notation expression.

Step 2: Conversion

The next step is the actual conversion. If \(n\) is positive, move the decimal point in \(a\) to the right by \(n\) places. If \(n\) is negative, move the decimal point in \(a\) to the left by \(|n|\) places. The resulting number will be in decimal notation.

Step 4: Example

Let's use an example to illustrate this. Suppose we want to convert \(3.5 \times 10^3\) from scientific to decimal notation. Here, \(a = 3.5\) and \(n = 3\), which is positive. Therefore, we move the decimal point in \(3.5\) three places to the right to get \(3500\). Hence, \(3.5 \times 10^3\) in decimal notation is \(3500\).