Question

Evaluate$(4.15\times {10}^3)(3.0\times {10}^6)$ . Express the result in scientific notation.

Short answer

The scientific notation of the given number is $1.245\times {10}^{10}$.

Step-by-step solution

Step 1. Write down the given expression.

The given number is $(4.15\times {10}^3)(3.0\times {10}^6)$.

Step 2. Expressing the given number in scientific notation.

The number $(4.15\times {10}^3)(3.0\times {10}^6)$ in scientific notation is expressed as:

$\begin{array}{c}(4.15\times {10}^3)(3.0\times {10}^6)=(4.15\times 3.0)({10}^3\times {10}^6)\\ =12.45\times {\left(10\right)}^9\\ =12.45\times {10}^9\times \frac{10}{10}\mathrm{....}\left(\begin{array}{l}\text{Multiplyand}\\ \text{divideby}10\end{array}\right)\\ =1.245\times {10}^{10}\end{array}$

Step 3. Conclusion.

The scientific notation of the given number is $1.245\times {10}^{10}$.