Write the answer in proper scientific notation: $\newline$ $\frac{1}{500 x 10^{4}}$

Full solution

Q. Write the answer in proper scientific notation:

\newline

\frac{1}{500 x 10^{4}}

Express in Scientific Notation: First, we need to express $500$ in scientific notation. $\newline$ $500$ can be written as $5 \times 10^2$ because $5$ times $10$ squared equals $500$ .
Rewrite with Scientific Notation: Now, we rewrite the original expression using the scientific notation for $500$ . The expression becomes $(1)/(5 \times 10^2 \times 10^4)$ .
Combine Powers of $10$ : Next, we combine the powers of $10$ using the rule of exponents that states when you multiply powers of $10$ , you add the exponents. $\newline$ So, $10^2 \times 10^4$ becomes $10^{(2+4)}$ , which is $10^6$ .
Adjust Coefficient: The expression is now $(1)/(5 \times 10^6)$ . To write this in scientific notation, we need to have a number between $1$ and $10$ multiplied by a power of $10$ . Since $5$ is already between $1$ and $10$ , we can write the expression as $1 \times 10^{-6}$ divided by $5$ .
Divide in Scientific Notation: To divide by $5$ in scientific notation, we can adjust the coefficient from $1$ to $1/5$ . $1/5$ is $0.2$ , so the expression in scientific notation is $0.2 \times 10^{-6}$ .
Check Proper Notation: Finally, we check if $0.2 \times 10^{-6}$ is in proper scientific notation. Since $0.2$ is between $1$ and $10$ , and the power of $10$ is written as an exponent, the expression is in proper scientific notation.