Question

James had a peach that was
\[98 \text{ mm}\] in diameter. One day he watered it with a magical solution, and it grew to
\[188{,}869 \text{ mm}\] in diameter.
Approximately how many times as large did the diameter of the peach become after James watered it?
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[2 \cdot10^3\]
A
\[2 \cdot10^3\]
(Choice B)
\[9 \cdot10^3\]
B
\[9 \cdot10^3\]
(Choice C)
\[2 \cdot10^4\]
C
\[2 \cdot10^4\]
(Choice D)
\[9 \cdot10^4\]
D
\[9 \cdot10^4\]

Answer 1

To determine how many times larger the diameter of the peach became after James watered it, we need to divide the final diameter by the initial diameter.

The initial diameter of the peach is \( 98 \text{ mm} \) and the final diameter is \( 188,869 \text{ mm} \).

Now, we calculate the ratio:

\[
\text{Ratio} = \frac{\text{Final Diameter}}{\text{Initial Diameter}} = \frac{188,869 \text{ mm}}{98 \text{ mm}}
\]

Calculating this:

\[
\text{Ratio} \approx \frac{188,869}{98} \approx 1924.08
\]

Thus, the diameter of the peach became approximately \( 1924 \) times larger after being watered.

Now, we need to express this in a scientific form. \( 1924 \) can be written as \( 1.924 \times 10^3 \), which simplifies to approximately \( 2 \cdot 10^3 \).

Therefore, the correct answer is:

**(Choice A) \( 2 \cdot 10^3 \)**.