Question

this question has two parts. first, answer part a. then, answer part b.
part a
peggy calculated the distance that light travels in 1 hour and wrote the result as 670,600,000 = 0.6706 × 10⁹ miles.
describe the mistake that peggy made in representing her answer in scientific notation.
keyboard help

part b
rewrite peggy’s answer in scientific notation correctly. describe the steps needed to rewrite her answer in the proper form.
keyboard help

Explanation:

Part A

Scientific notation requires a coefficient between 1 and 10. Peggy used 0.6706, which is less than 1, violating this rule. When she converted 670,600,000 to $0.6706 \times 10^9$, she incorrectly set the coefficient below 1 instead of adjusting the exponent to keep the coefficient in the valid range.

Step1: Identify valid coefficient

Move decimal in 670,600,000 to get $6.706$ (1 ≤ 6.706 < 10).

Step2: Count decimal shifts

Decimal moved 8 places left, so exponent is 8.

Step3: Write proper notation

Combine coefficient and power of 10.

Answer:

Peggy's mistake is that the coefficient in her scientific notation ($0.6706$) is less than 1. Scientific notation requires the coefficient to be a number between 1 and 10, not including 10.

---

Part B