Question

7 $\frac{5\times10^{7}}{2.63\times10^{-2}}$ 8 $\frac{4.2\times10^{4}}{3.5\times10^{-4}}$ 9 $\frac{7.1\times10^{6}}{8.2\times10^{5}}$

Explanation:

Step1: Divide the coefficients

For $\frac{5\times 10^{7}}{2.63\times 10^{- 2}}$, divide the non - power - of - 10 parts: $\frac{5}{2.63}\approx1.901$. Divide the powers of 10 using the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, so $\frac{10^{7}}{10^{-2}}=10^{7-(-2)} = 10^{9}$. Then the result is $1.901\times 10^{9}$.
For $\frac{4.2\times 10^{4}}{3.5\times 10^{-4}}$, divide the coefficients: $\frac{4.2}{3.5} = 1.2$. Divide the powers of 10: $\frac{10^{4}}{10^{-4}}=10^{4-(-4)}=10^{8}$. So the result is $1.2\times 10^{8}$.
For $\frac{7.1\times 10^{6}}{8.2\times 10^{5}}$, divide the coefficients: $\frac{7.1}{8.2}\approx0.866$. Divide the powers of 10: $\frac{10^{6}}{10^{5}}=10^{6 - 5}=10^{1}$. So the result is $0.866\times 10^{1}=8.66$.

Step2: Write the final answers in scientific notation

For the first one, $1.901\times 10^{9}$ (already in scientific notation).
For the second one, $1.2\times 10^{8}$ (already in scientific notation).
For the third one, $8.66$ can be written as $8.66\times 10^{0}$

Answer:

1. $1.901\times 10^{9}$
2. $1.2\times 10^{8}$
3. $8.66\times 10^{0}$