What is the distance in km of quasar from whigh light takes 3 billion years to reach us? `c=3xx10^(5)` km/s.

Explanation

To find the distance of a quasar from which light takes 3 billion years to reach us, we can use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 1: Convert time from years to seconds
Given that the time is 3 billion years, we can express this in scientific notation:

\[ \text{Time} = 3 \times 10^9 \text{ years} \]

Now, we need to convert years into seconds. We know that:

- 1 year = 365.25 days (to account for leap years)
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds

So, we can calculate the total number of seconds in 3 billion years:

\[ \text{Time in seconds} = 3 \times 10^9 \text{ years} \times 365.25 \text{ days/year} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]

Calculating this step-by-step:

1. Calculate the number of seconds in one year:
\[ 365.25 \times 24 \times 60 \times 60 = 31,557,600 \text{ seconds/year} \]

2. Now multiply by 3 billion:
\[ \text{Time in seconds} = 3 \times 10^9 \times 31,557,600 \approx 9.460 \times 10^{16} \text{ seconds} \]

### Step 2: Calculate the distance
Now we can use the speed of light, which is given as:

\[ c = 3 \times 10^5 \text{ km/s} \]

Now, we can calculate the distance:

\[ \text{Distance} = c \times \text{Time} \]

Substituting the values:

\[ \text{Distance} = 3 \times 10^5 \text{ km/s} \times 9.460 \times 10^{16} \text{ seconds} \]

Calculating this gives:

\[ \text{Distance} \approx 2.838 \times 10^{22} \text{ km} \]

### Final Result
Thus, the distance of the quasar is approximately:

\[ \text{Distance} \approx 2.84 \times 10^{22} \text{ km} \]