Question

question
what is the quotient of $7.584 \times 10^9$ and $7.9 \times 10^2$ expressed in scientific notation?

answer attempt 1 out of 2

answer: $\square \times 10^{\square}$ submit answer

Explanation:

Step1: Divide the coefficients

To find the quotient of the two numbers in scientific notation, we first divide the coefficients. The coefficients are \(7.584\) and \(7.9\). So we calculate \(\frac{7.584}{7.9}\).
\[
\frac{7.584}{7.9} = 0.96
\]

Step2: Divide the powers of 10

Next, we divide the powers of 10. When dividing numbers in scientific notation with the same base (in this case, base 10), we subtract the exponents. So we have \(10^{9} \div 10^{2}\), which is \(10^{9 - 2}\).
\[
10^{9 - 2} = 10^{7}
\]

Step3: Combine the results

Now we combine the results from Step 1 and Step 2. The coefficient is \(0.96\) and the power of 10 is \(10^{7}\), so the quotient in scientific notation is \(0.96\times10^{7}\). But we need to adjust the coefficient to be between 1 and 10. We can rewrite \(0.96\times10^{7}\) as \(9.6\times10^{6}\) (by moving the decimal point one place to the right and decreasing the exponent by 1).

Answer:

\(9.6\times10^{6}\)