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? $\newline$ Choose $1$ answer: $\newline$ (A) $2\times10^{3}$ $\newline$ (B) $9\times10^{3}$ $\newline$ (C) $2\times10^{4}$ $\newline$ (D) $9\times10^{4}$

Full solution

Q. 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?

\newline

Choose

1

answer:

\newline

(A)

2\times10^{3}

\newline

(B)

9\times10^{3}

\newline

(C)

2\times10^{4}

\newline

(D)

9\times10^{4}

Calculate Diameter Increase: Calculate the increase in the diameter of the peach. $\newline$ Original diameter = $98\,\text{mm}$ $\newline$ New diameter = $188,869\,\text{mm}$ $\newline$ Increase = New diameter - Original diameter $\newline$ Increase = $188,869\,\text{mm} - 98\,\text{mm}$ $\newline$ Increase = $188,771\,\text{mm}$
Determine Times Larger: Determine how many times larger the new diameter is compared to the original diameter. $\newline$ Times larger = New diameter / Original diameter $\newline$ Times larger = $188,869\,\text{mm}$ / $98\,\text{mm}$
Perform Division: Perform the division to find the approximate factor of increase. $\newline$ Times larger $\approx \frac{188,869}{98}$ $\newline$ Times larger $\approx 1,927.23$
Round Factor of Increase: Round the factor of increase to the nearest power of $10$ to match the answer choices. $\newline$ $1,927.23$ is closest to $2,000$ , which is $2 \times 10^3$ .
Select Correct Answer: Select the correct answer from the given choices. $\newline$ The correct answer is (A) $2\times10^{3}$ , which is the closest power of $10$ to our calculated value of approximately $1,927.23$ .