What is 52,683 written in scientific notation? A. 52.683 x 10 B. 0.52683 x 10 C. 5.2683 x 10 D. 5.2683 x 10

Break Down the Problem

1. Identify the number to be converted to scientific notation: 52,683.
2. Recall the format for scientific notation: It is expressed as $a \times 10^n$ where $1 \leq a < 10$ and $n$ is an integer.

Relevant Concepts

1. Convert 52,683 into the form $a \times 10^n$.
2. Determine the appropriate value for $n$.

Analysis and Detail

1. Move the decimal point in 52,683 to the left until only one non-zero digit remains on the left.
   • Moving the decimal point 4 places to the left gives: $5.2683$
2. The decimal shift indicates the exponent $n$:
   • Since we moved the decimal 4 places to the left, $n = 4$.
3. Combine both parts to write in scientific notation:
   • Therefore, $52,683 = 5.2683 \times 10^4$.

Verify and Summarize

1. Check that $5.2683$ is between 1 and 10.
   • Confirmed, $1 \leq 5.2683 < 10$.
2. Verify that moving the decimal point back gives the original number: $5.2683 \times 10^4 = 52,683$
   • This confirms the correctness.

Final Answer

Thus, the scientific notation for 52,683 is $5.2683 \times 10^4$. The correct answer is C. $5.2683 \times 10^4$.