Question

How do you write ${10^{ - 1}}$ in decimal form?

Answer 1

Hint: Here we must know that ${a^{ - b}}$ can be written in the form of $\dfrac{1}{{{a^b}}}$and also that ${a^b} = a.a.a.a........{\text{b times}}$
Hence by using this property we can simplify the above-given term and get the value in the form of the decimal point.

Complete step-by-step answer:
Here we are given the term ${10^{ - 1}}$ which we need to convert to decimal. So first of all we need to convert this value which in the form of the exponent and the degree into the form where we have numerator and denominator and then we can cancel those terms in the numerator and denominator with the common factor of them and hence we can further get the simplest form of the given term or the fraction.
We know that ${a^{ - b}}$ can be written in the form of $\dfrac{1}{{{a^b}}}$ and therefore we can say that ${10^{ - 1}}$ can be written as $\dfrac{1}{{{{10}^1}}} = \dfrac{1}{{10}}$ and therefore we get the simplified form as $\dfrac{1}{{10}}$
Now we can divide this term $1{\text{ by 10}}$ and get the value in the form of decimal of the fraction $\dfrac{1}{{10}}$
So we know that when we divide any number with ${10^n}$ we only need to shift the decimal form right to left in the numerator till the $n{\text{th}}$ term from the right.
Here we have $\dfrac{1}{{10}}$ as the fraction and we can compare the denominator with ${10^n}$. So we get that $n = 1$ and therefore we need to move the numerator from right to left $n{\text{th}}$ term and then put decimal over there. So here when we move from right to left in the numerator which is \[1\] we get the result as $0.1$

Hence we can write the value of ${10^{ - 1}}$ as $0.1$

Note: In these types of problems if we are given the term ${0.08^{ - 2}}$ then we must know what it's fraction will be.
We can write it as ${0.08^{ - 2}} = {\left( {\dfrac{8}{{100}}} \right)^{ - 2}} = {\left( {\dfrac{{100}}{8}} \right)^2} = \dfrac{{10000}}{{64}}$ and then we can simplify the fraction to get the simplest form of the fraction. Hence a student must know the correct way to write this form into the fraction form.