Verified Answer :
- Divide the total storage by the total number of customers: \(\frac{1.326 \times 10^{13}}{2.6 \times 10^4}\).
- Apply the division of coefficients and subtract exponents: \(0.51 \times 10^9\).
- Convert to standard scientific notation by adjusting the coefficient: \(5.1 \times 10^8\).
- The final result is \(\boxed{5.1 \times 10^8}\) bytes per customer.
Explanation
- Problem Analysis and Data Overview
The objective is to determine the average storage available per customer in an online data storage facility. We are provided with the total storage capacity, \(1.326 \times 10^{13}\) bytes, and the total number of customers, \(2.6 \times 10^4\). To find the storage per customer, we must divide the total storage by the total number of customers.
- Performing the Division and Simplifying Exponents
Let \(S = 1.326 \times 10^{13}\) bytes represent the total storage and \(C = 2.6 \times 10^4\) represent the number of customers. The storage per customer, \(B\), is given by:
\[B = \frac{S}{C} = \frac{1.326 \times 10^{13}}{2.6 \times 10^4}\]
Using the laws of exponents, we can separate the coefficients and the powers of ten:
\[B = \left( \frac{1.326}{2.6} \right) \times 10^{13-4}\]
Performing the division \(1.326 \div 2.6 = 0.51\), the expression becomes:
\[B = 0.51 \times 10^9\]
- Conversion to Standard Scientific Notation
Standard scientific notation requires the coefficient to be at least 1 and less than 10. Currently, we have \(0.51 \times 10^9\). To convert this, we adjust the coefficient and the exponent:
\[0.51 \times 10^9 = (5.1 \times 10^{-1}) \times 10^9 = 5.1 \times 10^{9-1} = 5.1 \times 10^8\]
Thus, each customer has \(5.1 \times 10^8\) bytes of storage available. The final answer is \(\boxed{5.1 \times 10^8}\).
Examples
Scientific notation is an essential tool in computing and data management, especially when handling massive datasets. For example, if a cloud service provider manages petabytes of data for millions of users, engineers use scientific notation to quickly estimate storage capacity, bandwidth requirements, and data transfer speeds. By converting very large or very small numbers into standard scientific form, calculations become much more manageable and less prone to errors when scaling infrastructure.