Question

To best estimate the quotient in scientific notation, what number should replace $m?$

Startfraction $6.33$ times $10$ Superscript $9$ Baseline Over $1.79$ times $10$ Superscript $5$ Baseline EndFraction almost equals $3$ times $10$ Superscript $m$

Answer 1

Estimate the quotient in scientific notation:

Step- 1: Write all these numbers in scientific notation:

The scientific notation of the given number is defined as:

$\frac{6.33\times {10}^9}{1.79\times {10}^5}\approx 3\times {10}^m$

Step- 2: Simplify the given notation:

Round off the coefficient of dividend and divisor in order to estimate the quotient:

Round $6.33$ to nearest ten:

$=6$

Round $1.79$ to nearest ten:

$=2$

Step-3: Rewrite the equation:

$$\begin{gathered} \frac{6\times {10}^9}{2\times {10}^5}\approx 3\times {10}^m \\ \Rightarrow 3\times {10}^{9-5}\approx 3\times {10}^m[a^m÷a^n=a^{m-n}] \end{gathered}$$

$\Rightarrow 3\times {10}^4\approx 3\times {10}^m$

$\Rightarrow {10}^4={10}^m$

Step- 4: Find the required values of $\mathit{m}$:

Compare the exponents to get the value of variable $m$.

$\begin{array}{rcl}& \Rightarrow & {10}^4={10}^m\\ & \Rightarrow & 4=m\end{array}$ $[\text{If bases are same, then the exponents must be equal]}$

Therefore, the value of $\mathit{m}$ is $\mathbf{4}\mathbf{.}$