If speed of light is `3.00xx10^8` m/s and 1 year =365.25 days, then 1 light year is

Options

A. `9.468xx10^15` m
B. 9.47 m
C. `9.47xx10^5` m
D. `9.46xx10^15` m

Answer

To find the distance that light travels in one year (1 light year), we can follow these steps:

### Step 1: Understand the definition of a light year
A light year is defined as the distance that light travels in one year.

### Step 2: Use the formula for distance
The formula for distance (s) is given by:
\[ s = \text{speed} \times \text{time} \]

### Step 3: Identify the speed of light
The speed of light is given as:
\[ \text{speed of light} = 3.00 \times 10^8 \text{ m/s} \]

### Step 4: Convert time from years to seconds
We know that:
- 1 year = 365.25 days
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds

Now, we can convert 1 year into seconds:
\[ 1 \text{ year} = 365.25 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]

Calculating this step-by-step:
1. Calculate the number of seconds in one day:
\[ 1 \text{ day} = 24 \times 60 \times 60 = 86400 \text{ seconds} \]
2. Now calculate the total seconds in one year:
\[ 1 \text{ year} = 365.25 \times 86400 \text{ seconds} = 31,557,600 \text{ seconds} \]

### Step 5: Calculate the distance traveled by light in one year
Now, substitute the values into the distance formula:
\[ s = (3.00 \times 10^8 \text{ m/s}) \times (31,557,600 \text{ s}) \]

### Step 6: Perform the multiplication
Calculating the distance:
\[ s = 3.00 \times 10^8 \times 31,557,600 \]
This can be simplified as:
\[ s = 3.00 \times 31.5576 \times 10^8 \times 10^7 = 9.46728 \times 10^{15} \text{ m} \]

### Step 7: Round off to appropriate significant figures
The speed of light has 3 significant figures, so we round off the answer to 3 significant figures:
\[ s \approx 9.46 \times 10^{15} \text{ m} \]

### Final Answer
Thus, 1 light year is approximately:
\[ \boxed{9.46 \times 10^{15} \text{ m}} \]

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