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

Question

Vedantu Content Team · Accepted Answer

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.

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