Question

calculate.\\(dfrac{7.2 \times 10^{-3}}{8 \times 10^{-7}}\\)\
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 we have $\frac{7.2}{8} \times \frac{10^{-3}}{10^{-7}}$.

Step2: Calculate the coefficient fraction

Calculate $\frac{7.2}{8}$. $7.2\div8 = 0.9$.

Step3: Calculate the power of 10 fraction

Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, for $\frac{10^{-3}}{10^{-7}}$, we get $10^{-3-(-7)}=10^{-3 + 7}=10^{4}$.

Step4: Multiply the results from Step2 and Step3

Multiply $0.9$ and $10^{4}$ to get $0.9\times10^{4}$. But in scientific notation, the coefficient should be between 1 and 10. So we rewrite $0.9$ as $9\times10^{-1}$. Then $9\times10^{-1}\times10^{4}=9\times10^{-1 + 4}=9\times10^{3}$.

Answer:

$9\times10^{3}$