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.
\[ \Rightarrow {a^{ - b}} = \dfrac{1}{{{a^b}}}\]
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.
\[ \Rightarrow \dfrac{1}{{{2^2}}}\]
In this, first, we calculate the denominator power. And the result is-
\[ \Rightarrow \dfrac{1}{4}\]
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.
\[ \Rightarrow \dfrac{1}{{{{10}^3}}}\]
In the above, first, we calculate the denominator power. And the result is
\[ \Rightarrow \dfrac{1}{{10 \times 10 \times 10}}\]
We simplify the above expression as below.
\[ \Rightarrow \dfrac{1}{{1000}}\]
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.