Question

How do you write ${{10}^{-5}}$ in decimal form?

Answer 1

This is a basic exponential concept problem. We will first remove the negative exponent and make it as a fraction. After making it as a fraction we will find the value of the denominator and then we will divide the numerator with the denominator. Then we will get the required decimal form.
Let us know how to get rid of a negative power.
To remove negative power in exponents we will use this formula .
${{a}^{-n}}=\dfrac{1}{{{a}^{n}}}$
Using this we can solve our problem easily.

Complete step by step answer:
Given expression is ${{10}^{-5}}$
Now we have to change the power to positive. As we already discussed we can use the above formula.
using the above discussed formula we can write our expression as
$\Rightarrow {{10}^{-5}}=\dfrac{1}{{{10}^{5}}}$
Now we have to find the value of the denominator.
By calculating the denominator value we will get
$\Rightarrow \dfrac{1}{100000}$
Normally we will check for the prime factors that will simplify the expression and then we will perform division. But in this case we don’t do that because here the numerator is 1 so it doesn’t have any prime factors so there will be no common factor that will divide both rather than 1 . so here we will divide the expression directly. By dividing numerator with denominator we will get
$\Rightarrow 0.00001$
So the decimal form of ${{10}^{-5}}$ is $0.00001$.

Note:
We can solve these types of problems easily but we have to be aware of calculation mistakes and conversions we do. then only we can get the correct answer otherwise we may get a different answer.