To express a light year in standard form, we follow these steps:
1. Identify the original number: the distance a light year represents is 9,463,700,000,000 kilometers.
2. Determine how to rewrite this number using scientific notation:
- Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.
- For 9,463,700,000,000, we can rewrite it as 9.4637 × 10¹².
3. Round the number to match the required significant figures:
- Here, we will round 9.4637 to three significant figures, which gives us 9.464.
4. Combine the rounded number with the power of ten:
- Hence, 9.464 × 10¹² km.
Therefore, in standard form, one light year is written as [tex]\( 9.464 \times 10^{12} \)[/tex] km.
