Certainly! To express a number in standard form (also known as scientific notation), you need to rewrite it as a product of a number between 1 and 10 and a power of 10. Let's convert the given distance of one light year, 9463700000000 km, into standard form.
Step-by-Step Solution:
1. Identify the significant figures: For the number 9463700000000, the significant figures are 9.4637. We want to place a decimal point after the first digit to obtain a number between 1 and 10.
2. Count the number of places the decimal point has moved: Start from the original position at the end of the number and move left until you reach the first digit. This is done to convert 9463700000000 into a number between 1 and 10.
9463700000000 → 9.4637 (Moving the decimal 12 places to the left).
3. Express the number in standard form: The initial number is [tex]\(9.4637\)[/tex] and you need to multiply it by [tex]\(10\)[/tex] raised to the number of places the decimal point was moved, which is 12.
Thus, [tex]\( 9463700000000 \)[/tex] km in standard form is [tex]\( 9.46 \times 10^{12} \)[/tex] km (rounding 9.4637 to two decimal places).
Therefore, one light year written in standard form is [tex]\( 9.46 \times 10^{12} \)[/tex] km.
