The number $518,000,000$ when expressed in scientific notation, equals

### Concept & Formula Standard scientific notation represents numbers in the form $a \times 10^n$, where $1 \le a < 10$ and $n$ is an integer representing the decimal shift. ### Step-by-Step Solution **Given:** $518,000,000$ To convert this to scientific notation, we need to place a decimal point after the first non-zero digit to create a number between 1 and 10. Place the decimal after the 5: $5.18$ Now, count how many places the decimal point moved from the end of $518,000,000$ (which is implicitly $518000000.0$) to get to $5.18$. The decimal shifted 8 places to the left. Because we moved the decimal to the left for a large number, the exponent $n$ is positive $8$. Result: $5.18 \times 10^8$ ### Exam Strategy & Shortcut Quickly eliminate options. A proper scientific notation must have a leading number strictly between 1 and 10. Options (a) and (b) start with $51.8$, which is an invalid format. Between (c) and (d), just count the digits after the 5. There are 8 digits, so the exponent is 8. ### Common Pitfall Choosing $51.8 \times 10^7$ because it mathematically equals the original number. However, standard scientific notation strictly requires the coefficient to be less than 10. ### Final Answer Therefore, the correct answer is $5.18 \times 10^8$.