Chapter 7.2, Problem 6LC

To determine

To find: Whether the given product is always, never or sometimes a number in scientific notation.

Answer to Problem 6LC

The given product is always in scientific notation.

Explanation of Solution

Given information:

The given two numbers in scientific notation are $a\times {10}^m$ and $b\times {10}^n$ , the product of both the given numbers be $ab\times {10}^{m+n}$ .

Calculation:

The given two numbers are is:

  $\begin{array}{l}a\times {10}^m\\ b\times {10}^n\end{array}$

The given expression of their product is:

  $ab\times {10}^{m+n}$

When the first product $ab$ is less than $10$ , then their product is always in scientific notation because scientific notation is way of representing the real numbers that are very large or very small in decimal form such that the absolute value $ab$ is greater than or equal to $1$ and less than $10$ so that large numbers can also be written using less digits.

Therefore, it implies that given product is always is in scientific notation.