Chapter SH, Problem 10.19E

To determine

Write the given expression in scientific notation.

Answer to Problem 10.19E

The Scientific notation of the given number is $3.77\times {10}^{10}$ .

Explanation of Solution

Given:

The given expression is $\left(8.90\times {10}^8\right)÷\left(2.36\times {10}^{-2}\right)$ .

Calculation:

Rewrite the given expression.

  $=\frac{8.90\times {10}^8}{2.36\times {10}^{-2}}$

  $=\frac{8.90}{2.36}\cdot \frac{{10}^8}{{10}^{-2}}$

To divide powers with the same base, subtract the exponents.

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

  $\begin{array}{l}=\frac{8.90}{2.36}\cdot \left({10}^{8-\left(-2\right)}\right)\\ =\frac{8.90}{2.36}\cdot \left({10}^{10}\right)\end{array}$

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.

  $=3.77\times {10}^{10}$

Scientific notation of the expression $=3.77\times {10}^{10}$

Hence the Scientific notation of the given expression is $3.77\times {10}^{10}$ .