Question

How do you write $94\times {{10}^{-7}}$ in expanded form?

Answer 1

Hint: The number given in the above question, which is equal to $94\times {{10}^{-7}}$, is in the terms of the power of ten. The number $94$ is being multiplied with ten raised to the power of $-7$. By writing it in the expanded form, we basically mean converting it into the decimal form. For writing it in the form of a decimal number, we need to use the property of the negative exponent, which is given by ${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$ so that the given number can be written as $\dfrac{94}{{{10}^{7}}}$. The power over a number refers to the number of times it is being multiplied. Therefore, ten is present seven times in the denominator, which in turn means that we need to divide $94$ by ten seven times. After this, the given number will be obtained in the expanded form.

Complete step by step answer:
Let us consider the number given in the above question as
$\Rightarrow n=94\times {{10}^{-7}}$
For writing the above number in the expanded form, we have to write it as a decimal number. For this, we use the negative exponent property given as ${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$. Therefore, the above equation will become
\[\begin{align}
  & \Rightarrow n=94\times \dfrac{1}{{{10}^{7}}} \\
 & \Rightarrow n=\dfrac{94}{{{10}^{7}}} \\
\end{align}\]
Now, we know that the power over a number indicates the number of times it is being multiplied. This means that the number $94$ is divided by ten for seven times. On dividing, we finally obtain
$\Rightarrow n=0.0000094$

Hence, the given number in the expanded form is written as $0.0000094$.

Note: The division by ten shifts the decimal point of the number to the left. Therefore, the division of $94$ by ${{10}^{7}}$ has shifted the decimal point seven units to the left, as we can note in the obtained expanded value. We can use this fact to quickly write down the final answer without committing the error.