When 299,790,000 is written in scientific notation as a × 10^k, what are the values of a and k?

• A. a = 2.9979, k = 7
• B. a = 29.979, k = 6
• C. a = 299.79, k = 6
• D. a = 2.9979, k = 8

Answer: (D)

Verified step by step guidance

1. Identify the number given: 299,790,000.
2. Recall that scientific notation expresses a number in the form \(a \times 10^{k}\), where \$1 \leq a < 10\( and \)k$ is an integer.
3. To write 299,790,000 in scientific notation, move the decimal point in the number to the left until only one non-zero digit remains to the left of the decimal point. Count how many places you move the decimal point; this count will be the exponent \(k\).
4. For 299,790,000, moving the decimal point 8 places to the left gives \$2.9979\(, so \)a = 2.9979\( and \)k = 8$.
5. Verify that \(a\) is between 1 and 10, and that multiplying \(a\) by \$10^{k}$ reconstructs the original number.