Question

calculate.
\\(\frac{5.6 \times 10^{-8}}{7 \times 10^{6}}\\)
write your answer in scientific notation.

Explanation:

Step1: Separate the coefficients and exponents

We can rewrite the fraction as the product of two fractions: one with the coefficients and one with the powers of 10. So, \(\frac{5.6\times 10^{-8}}{7\times 10^{6}}=\frac{5.6}{7}\times\frac{10^{-8}}{10^{6}}\)

Step2: Calculate the coefficient fraction

Calculate \(\frac{5.6}{7}\). \(5.6\div7 = 0.8\)

Step3: Calculate the exponent fraction

Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), for \(\frac{10^{-8}}{10^{6}}\), we have \(10^{-8-6}=10^{-14}\)

Step4: Combine the results

Now, multiply the results from Step 2 and Step 3: \(0.8\times10^{-14}\)
But in scientific notation, the coefficient should be between 1 and 10. So we rewrite \(0.8\) as \(8\times10^{-1}\). Then \(8\times10^{-1}\times10^{-14}=8\times10^{-1 - 14}=8\times10^{-15}\)

Answer:

\(8\times10^{-15}\)