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 complete 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.And make it 1 paragraph and copy and paste

Answer 1

Comet A’s tail is \( \frac{2.5 \times 10^6}{7 \times 10^5} \) kilometers long compared to Comet B’s tail. To simplify this calculation, we can first divide the coefficients: \( \frac{2.5}{7} \approx 0.3571 \). Next, we subtract the exponents in the scientific notation: \( 10^6 \div 10^5 = 10^{6-5} = 10^1 \). Therefore, the total comparison is \( 0.3571 \times 10^1 \), which we can convert to standard form by writing it as \( 3.571 \). Thus, Comet A’s tail is approximately 3.57 times longer than Comet B’s tail. Using scientific notation simplifies the comparison of large numbers, as it allows us to handle the significant figures (the coefficients) separately from the orders of magnitude (the exponents). This makes it easier to perform arithmetic operations, such as division, while minimizing the chances of error that might occur with very large standard form numbers.