Question

find the quotient. write your answer in scientific notation.\\((2.8 \times 10^4) \div (2.5 \times 10^6) = \square\\)

Explanation:

Step1: Separate coefficients and powers of 10

We can rewrite the division as the quotient of the coefficients times the quotient of the powers of 10. So, \((2.8\times10^{4})\div(2.5\times10^{6})=\frac{2.8}{2.5}\times\frac{10^{4}}{10^{6}}\)

Step2: Divide the coefficients

Calculate \(\frac{2.8}{2.5}\). \(2.8\div2.5 = 1.12\)

Step3: Divide the powers of 10

Using the rule of exponents \(a^{m}\div a^{n}=a^{m - n}\), we have \(\frac{10^{4}}{10^{6}}=10^{4-6}=10^{-2}\)

Step4: Multiply the results

Multiply the result from Step 2 and Step 3: \(1.12\times10^{-2}\)

Answer:

\(1.12\times 10^{-2}\)