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3. A light year is the distance that light travels in one year, 9,463,700,000,000 km.

(a) Write one light year in standard form. [tex][2][/tex]

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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.
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