Question

calculate.
\\(\frac{3.5 \times 10^{-7}}{5 \times 10^{3}}\\)
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: $\frac{3.5\times 10^{-7}}{5\times 10^{3}}=\frac{3.5}{5}\times\frac{10^{-7}}{10^{3}}$

Step2: Calculate the coefficient ratio

Calculate $\frac{3.5}{5}$: $\frac{3.5}{5} = 0.7$

Step3: Calculate the power of 10 ratio

Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, for $\frac{10^{-7}}{10^{3}}$, we have $10^{-7-3}=10^{-10}$

Step4: Combine the results

Now we combine the coefficient and the power of 10: $0.7\times 10^{-10}$
But in scientific notation, the coefficient should be between 1 and 10. So we rewrite $0.7$ as $7\times 10^{- 1}$. Then $7\times 10^{-1}\times 10^{-10}=7\times 10^{-1 - 10}=7\times 10^{-11}$

Answer:

$7\times 10^{-11}$