Question

How do you divide $\dfrac{{0.8 \times {{10}^{ - 7}}}}{{4 \times {{10}^{ - 4}}}}$?

Answer 1

Hint: According to given in the question we have to divide the given fraction $\dfrac{{0.8 \times {{10}^{ - 7}}}}{{4 \times {{10}^{ - 4}}}}$ which is as mentioned in the question. So, first of all to determine the division of the given fraction we have to rearrange the terms of the fraction which can be done with the help of the formula as mentioned below:

Formula used: $ \dfrac{1}{{{x^{ - 1}}}} = x.................(A)$
Now, after rearranging the terms of the fraction we have to solve it further which can be done with the help of the formula which is as mentioned below:
$ \Rightarrow {x^n} \times {x^m} = {x^{m + n}}.....................(B)$
Hence, with the help of the formula above we can determine the values of the terms having positive and negative power.
Now, we have to solve the decimal numbers which can be done by simple division to obtain the required division of the given fraction.

Complete step-by-step solution:
Step 1: First of all to determine the division of the given fraction we have to rearrange the terms of the fraction which can be done with the help of the formula (A) as mentioned in the solution hint. Hence,
$ = \dfrac{{0.8 \times {{10}^{ - 7}} \times {{10}^{ + 4}}}}{4}$
Step 2: Now, after rearranging the terms of the fraction we have to solve it further which can be done with the help of the formula (B) which is as mentioned in the solution hint. Hence,
\[
   = \dfrac{{0.8 \times {{10}^{ - 7 + 4}}}}{4} \\
   = \dfrac{{0.8 \times {{10}^{ - 3}}}}{4}
 \]
Step 3: Now, we have to solve the decimal numbers which can be done by simple division to obtain the required division of the given fraction. Hence,
\[ = 0.2 \times {10^{ - 3}}\]

Hence, with the help of the formula (A) and (B) we have determined the division of $\dfrac{{0.8 \times {{10}^{ - 7}}}}{{4 \times {{10}^{ - 4}}}}$ which is \[ = 0.2 \times {10^{ - 3}}\].

Note: It is necessary that we have to rearrange the terms of the given function which can be done by $\dfrac{1}{{{x^{ - 1}}}} = x$ which is already mentioned.
To solve the powers of the given function it is necessary that we have to use the formula ${x^n} \times {x^m} = {x^{m + n}}$ to determine the solution of the given function.