Question

How do you write $${10}^{-3}$$ in decimal form?

Answer 1

Hint: In this question, we find the decimal form of the negative power of a number. For solving this question, we used the low of indices. Low indices signify that if a number has a negative power then it is reciprocated with the positive index for the same variable. It is expressed as below.
$$\Rightarrow a^{-b}={\displaystyle \frac{1}{a^b}}$$
Where, $$a$$ is a number, which has the power of $$-b$$.
$$b$$ Is the power of a number.

Complete step by step answer:
As we know that in algebra, there are some constant and variable uses. First, we know about constants and variables.
Constant: the constant is the value that does not change.
Variable: the variable is the value that is changed.
Let’s take an example, if a number $$2^{-2}$$has the negative power. Then according to low indices, we write this as the fraction form.
The fraction form is given below.
$$\Rightarrow {\displaystyle \frac{1}{2^2}}$$
In this, first, we calculate the denominator power. And the result is-
$$\Rightarrow {\displaystyle \frac{1}{4}}$$
Then divide the numerator with the denominator and the result will become as below.
$$\Rightarrow 0.25$$
In this example, we can easily convert the negative power of a number into a decimal.
Let’s come to the question, is the question we convert a negative power of a number in the decimal form. And the negative power of numbers is given below.
$$\Rightarrow {10}^{-3}$$
We write this number in fraction form according to low indices.
$$\Rightarrow {\displaystyle \frac{1}{{10}^3}}$$
In the above, first, we calculate the denominator power. And the result is
$$\Rightarrow {\displaystyle \frac{1}{10\times 10\times 10}}$$
We simplify the above expression as below.
$$\Rightarrow {\displaystyle \frac{1}{1000}}$$
Then divide the numerator with the denominator and the result will become as below.
$$\therefore 0.001$$

Therefore, the decimal form of $${10}^{-3}$$ is$$0.001$$.

Note: As we know that if the number has a negative power. We want to convert it into decimal form then first we convert the negative power of the number in the form of a fraction (numerator and denominator form) with the positive index.