Problem 1 - Algebra 1: Concepts and Skills

Question

Is the number \(12.38 \times 10^{2}\) in scientific notation? Explain.

Step-by-Step Solution

Answer

No, the number \(12.38 \times 10^{2}\) is not in scientific notation. In scientific notation the coefficient is always between 1 and 10, but 12.38 is not.

Step 1: Identify the components of the number

The number to analyze is \(12.38 \times 10^{2}\). It can be broken down into \(a = 12.38\) and \(n = 2\).

Step 2: Apply the definition of scientific notation feature for number \(a\)

By applying the definition of scientific notation, we need to evaluate if \(1 \leq a < 10\), for our number \(a = 12.38\). It can be observed that the condition \(1 \leq a < 10\) is not satisfied by the number \(12.38\). Thus, the number \(12.38 \times 10^{2}\) is not in correct scientific notation.