Chapter SH, Problem 10.12E

To determine

Write the given expression in scientific notation.

Answer to Problem 10.12E

The Scientific notation of the given number is $3\times {10}^1$ .

Explanation of Solution

Given:

The given expression is $\left(2.5\times {10}^{-3}\right)\left(1.2\times {10}^4\right)$ .

Calculation:

Rewrite the given expression.

  $\left(2.5\times 1.2\right)\left({10}^{-3}\times {10}^4\right)$

To multiply powers with the same base, add the exponents.

  $a^m\cdot a^n=a^{m+n}$ , where $a\ne 0$ and $m$ and $n$ are rational numbers.

  $\begin{array}{l}=\left(2.5\times 1.2\right)\left({10}^{-3+4}\right)\\ =\left(2.5\times 1.2\right)\left(10\right)\end{array}$

Scientific notation $\to$ it is a standard way of writing very large and very small numbers.

The form of the Scientific notation is

  $n\times {10}^m$ , where $1\le n<10$ and $m$ is an integer.

Remove parentheses.

  $\begin{array}{l}=3.00\times {10}^1\\ =3\times {10}^1\end{array}$

Scientific notation of the expression $=3\times {10}^1$

Hence the Scientific notation of the given expression is $3\times {10}^1$ .