Question

A cell phone weighs about 2.8 times 10 Superscript n pounds. Which value of n is most reasonable?
Negative 3
Negative 1
0
1

Answer 1

To determine which value of \( n \) is most reasonable for the weight of a cell phone, we can analyze the options given:

1. **If \( n = -3 \)**:
\[
2.8 \times 10^{-3} \text{ pounds} = 0.0028 \text{ pounds}
\]

2. **If \( n = -1 \)**:
\[
2.8 \times 10^{-1} \text{ pounds} = 0.28 \text{ pounds}
\]

3. **If \( n = 0 \)**:
\[
2.8 \times 10^{0} \text{ pounds} = 2.8 \text{ pounds}
\]

4. **If \( n = 1 \)**:
\[
2.8 \times 10^{1} \text{ pounds} = 28 \text{ pounds}
\]

Now analyzing the potential weights:
- A cell phone weighing **0.0028 pounds** (if \( n = -3 \)) is unrealistically light, as that is about the weight of a piece of paper.
- A weight of **0.28 pounds** (if \( n = -1 \)) is quite reasonable for most modern smartphones as they typically weigh around 5 to 7 ounces (which is close to 0.28 pounds).
- A weight of **2.8 pounds** (if \( n = 0 \)) is heavier than most smartphones, though some phones with cases or additional features might approach this weight.
- A weight of **28 pounds** (if \( n = 1 \)) is far too heavy for a cell phone.

Thus, the most reasonable value for \( n \) is **-1**.