To convert [tex]\(1.234 \frac{ \text{km} }{ \text{day} }\)[/tex] to base SI units, we need to express the speed in meters per second (m/s). Here's a step-by-step guide to achieving this:
1. Convert kilometers to meters:
- We know that [tex]\(1 \text{ km} = 1000 \text{ meters}\)[/tex].
- Therefore, [tex]\(1.234 \text{ km}\)[/tex] is equal to [tex]\(1.234 \times 1000 \text{ meters}\)[/tex].
[tex]\[
1.234 \text{ km} = 1.234 \times 1000 \text{ meters} = 1234 \text{ meters}
\][/tex]
2. Convert days to seconds:
- We know that [tex]\(1 \text{ day} = 24 \text{ hours}\)[/tex], [tex]\(1 \text{ hour} = 60 \text{ minutes}\)[/tex], and [tex]\(1 \text{ minute} = 60 \text{ seconds}\)[/tex].
- Therefore, [tex]\(1 \text{ day} = 24 \times 60 \times 60 \text{ seconds} = 86400 \text{ seconds}\)[/tex].
[tex]\[
1 \text{ day} = 86400 \text{ seconds}
\][/tex]
3. Convert meters per day to meters per second:
- We already have that [tex]\(1.234 \text{ km/day} = 1234 \text{ meters/day}\)[/tex].
- To convert meters per day to meters per second, we divide by the number of seconds in a day:
[tex]\[
\frac{1234 \text{ meters}}{86400 \text{ seconds}}
\][/tex]
4. Calculate the result and express it in scientific notation:
- Performing the division:
[tex]\[
\frac{1234}{86400} \approx 0.01428 \text{ meters/second}
\][/tex]
- To express [tex]\(0.01428\)[/tex] in scientific notation, we write it as [tex]\(1.428 \times 10^{-2}\)[/tex].
Therefore, the final result of converting [tex]\(1.234 \frac{ \text{km} }{ \text{day} }\)[/tex] to [tex]\(\text{m/s}\)[/tex] in standard form scientific notation is:
[tex]\[
\boxed{1.428 \times 10^{-2}}
\][/tex]
