Question

(\frac{6.94\times10^{-4}}{7.98\times10^{6}-1.00\times10^{-8}}=\boxed{quad})

Explanation:

Step1: Simplify the denominator

First, calculate the value of the denominator \(7.98\times10^{6}-1.00\times10^{-8}\). Since \(1.00\times10^{-8}\) is much smaller than \(7.98\times10^{6}\), we can approximate the denominator as \(7.98\times10^{6}\) (because \(1.00\times10^{-8}\) has a negligible effect on the value of \(7.98\times10^{6}\)).

Step2: Rewrite the fraction

Now the expression becomes \(\frac{6.94\times10^{-4}}{7.98\times10^{6}}\).

Step3: Divide the coefficients and subtract the exponents of 10

Divide the coefficients: \(\frac{6.94}{7.98}\approx0.8697\).
Subtract the exponents of 10: \(10^{-4 - 6}=10^{-10}\).

Step4: Combine the results

Multiply the coefficient and the power of 10: \(0.8697\times10^{-10}\).
Convert to scientific notation: \(8.70\times10^{-11}\) (rounding to three significant figures).

Answer:

\(8.70\times10^{-11}\) (or approximately \(8.7\times10^{-11}\) depending on the required precision)