Question

examples multiply or divide. 1. (8.2×10²)×43 2. (1.83×10⁶)÷30

Explanation:

Step1: Simplify the first - part

First, calculate $(8.2\times10^{2})$. Since $10^{2}=100$, then $8.2\times10^{2}=8.2\times100 = 820$.

Step2: Multiply the results

Multiply the result of step 1 by 43. So, $820\times43=(800 + 20)\times43=800\times43+20\times43=34400+860 = 35260$.

Step3: Simplify the second - part

For $(1.83\times10^{6})\div30$. First, rewrite 30 as $3\times10^{1}$. Then, $(1.83\times10^{6})\div(3\times10^{1})=\frac{1.83}{3}\times\frac{10^{6}}{10^{1}}$.

Step4: Calculate the division of coefficients and exponents

$\frac{1.83}{3}=0.61$ and $\frac{10^{6}}{10^{1}}=10^{6 - 1}=10^{5}$ according to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$. So, $(1.83\times10^{6})\div30=0.61\times10^{5}=6.1\times10^{4}$.

Answer:

The result of $(8.2\times10^{2})\times43$ is 35260 and the result of $(1.83\times10^{6})\div30$ is $6.1\times10^{4}$