Question

Nick found the quotient of 8.64 and 1.25 × 105. His work is shown below.

1. (8.64 × 101)
(1.25 × 105)

2. (8.64
1.25
) (101
105
)

3. 6.912 × 10–4

Analyze Nick’s solution. Is he correct? If not, what was his mistake?
Yes, Nick is correct.
No, the power multiplied to 8.64 should have an exponent of 0.
No, he needed to subtract the coefficients.
No, he needed to add the exponents.

Answer 1

To analyze Nick's solution, let's break it down step by step.

1. He starts with \( \frac{8.64}{1.25 \times 10^5} \), and he rewrites \( 8.64 \) as \( 8.64 \times 10^1 \). This step is correct and helps him express both the numerator and denominator in a proper scientific notation form.

2. In step 2, he separates the coefficients and the powers of ten:
\[
\frac{8.64 \times 10^1}{1.25 \times 10^5} = \frac{8.64}{1.25} \times \frac{10^1}{10^5}
\]

3. He calculates \( \frac{8.64}{1.25} \). The result of this calculation is \( 6.912 \), which is correct.

4. Next, he evaluates the powers of ten:
\[
\frac{10^1}{10^5} = 10^{1 - 5} = 10^{-4}
\]

5. Now, combining the coefficient and the power of ten:
\[
6.912 \times 10^{-4}
\]

Thus, Nick's final answer is \( 6.912 \times 10^{-4} \).

Now, let's evaluate the options provided:

- **Yes, Nick is correct.** (This is true.)
- **No, the power multiplied to 8.64 should have an exponent of 0.** (Incorrect, because he correctly expressed it as \( 10^1 \).)
- **No, he needed to subtract the coefficients.** (Incorrect, his operation on coefficients was correct.)
- **No, he needed to add the exponents.** (Incorrect because, in division, exponents are subtracted.)

Therefore, the correct conclusion is **Yes, Nick is correct.**