Question
A space agency is tracking two comets:
Comet A has a tail length of 2.5 × 10⁶ kilometers.
Comet B has a tail length of 7 × 10⁵ kilometers.
Question:
Using 1-2 complete, short sentences, explain how many times longer Comet A’s tail is compared to Comet B’s tail. Show your calculations in scientific notation, and explain why using scientific notation makes it easier to perform this comparison instead of using standard form. Include any reasoning about the exponents and coefficients in your explanation.
Comet A has a tail length of 2.5 × 10⁶ kilometers.
Comet B has a tail length of 7 × 10⁵ kilometers.
Question:
Using 1-2 complete, short sentences, explain how many times longer Comet A’s tail is compared to Comet B’s tail. Show your calculations in scientific notation, and explain why using scientific notation makes it easier to perform this comparison instead of using standard form. Include any reasoning about the exponents and coefficients in your explanation.
Answers
GPT-4o mini
To find how many times longer Comet A’s tail is compared to Comet B’s tail, we divide the lengths expressed in scientific notation:
\[
\frac{2.5 \times 10^6 \text{ km}}{7 \times 10^5 \text{ km}} = \frac{2.5}{7} \times 10^{6-5} = 0.3571 \times 10^1 = 3.571.
\]
Thus, Comet A’s tail is approximately 3.57 times longer than Comet B’s tail. Using scientific notation simplifies the division by allowing us to handle the coefficients and exponents separately: the coefficients (2.5 and 7) are divided as simple numbers, and the exponents (6 and 5) are subtracted, making calculations straightforward without dealing with large numbers directly.
\[
\frac{2.5 \times 10^6 \text{ km}}{7 \times 10^5 \text{ km}} = \frac{2.5}{7} \times 10^{6-5} = 0.3571 \times 10^1 = 3.571.
\]
Thus, Comet A’s tail is approximately 3.57 times longer than Comet B’s tail. Using scientific notation simplifies the division by allowing us to handle the coefficients and exponents separately: the coefficients (2.5 and 7) are divided as simple numbers, and the exponents (6 and 5) are subtracted, making calculations straightforward without dealing with large numbers directly.