Question

question
what is the product of $6.8 \times 10^4$ and $9.3 \times 10^6$ expressed in scientific notation?
answer attempt 1 out of 2
answer: $\square \times 10^{\square}$ submit answer

Explanation:

Step1: Multiply the coefficients

Multiply \(6.8\) and \(9.3\).
\(6.8\times9.3 = 63.24\)

Step2: Add the exponents of 10

When multiplying numbers in scientific notation, we add the exponents of \(10\). So for \(10^{4}\) and \(10^{6}\), we add \(4\) and \(6\).
\(10^{4}\times10^{6}=10^{4 + 6}=10^{10}\)

Step3: Combine the results

Now we combine the coefficient and the power of \(10\) from the previous steps. But we need to check if the coefficient is in the correct range for scientific notation (between \(1\) and \(10\)).
We have \(63.24\times10^{10}\). To convert \(63.24\) to a number between \(1\) and \(10\), we can write it as \(6.324\times10^{1}\). Then we multiply this by \(10^{10}\).
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we get \(6.324\times10^{1}\times10^{10}=6.324\times10^{11}\)

Answer:

\(6.324\times 10^{11}\)