Answer: 25,200.
Explanation:
1) Starting with: 4.659 × 10⁴ - 2.14 × 10⁴
2) Significant figures need to be considered.
Because the powers are equal (10⁴), the decimal values can be subtracted directly. However, it is essential to first check significant figures and the count of decimal places.
3) The figure 4.659 × 10⁴ has four significant digits (4, 6, 5, and 9), whereas 2.14 × 10⁴ contains three significant digits (2, 1, and 4).
4) When adding or subtracting values with a different number of decimal places, the answer must reflect the same number of decimal places as the number with the least amount of decimal precision.
5) Prior to performing subtraction, it is necessary to round the numbers to the least decimal places. Given that 2.14 has two decimal places and 4.659 has three, round 4.659 to 4.66.
6) Now perform the subtraction 4.66 - 2.14 = 2.52
7) Then multiply by the power of 10: 2.52 × 10⁴ = 25,200. This is the final answer.
