Question

calculate.
\\(\frac{9 \times 10^9}{3 \times 10^2}\\)
write your answer in scientific notation.

Explanation:

Step1: Separate coefficients and powers of 10

We can split the fraction into the ratio of the coefficients and the ratio of the powers of 10. So, \(\frac{9\times 10^{9}}{3\times 10^{2}}=\frac{9}{3}\times\frac{10^{9}}{10^{2}}\)

Step2: Simplify the coefficient

Simplify \(\frac{9}{3}\), which equals \(3\).

Step3: Simplify the power of 10

Using the rule of exponents \(\frac{a^{m}}{a^{n}} = a^{m - n}\), for \(\frac{10^{9}}{10^{2}}\), we have \(10^{9-2}=10^{7}\)

Step4: Combine the results

Multiply the simplified coefficient and the simplified power of 10: \(3\times10^{7}\)

Answer:

\(3\times 10^{7}\)