To convert seconds into minutes using dimensional analysis, we will use the fact that:
1 minute = 60 seconds
We can set up the conversion as follows:
- Start with the given quantity in seconds:
\[ 230 , \text{seconds} \]
- Use the conversion factor to change seconds to minutes. To do this, we'll multiply by a fraction that represents the conversion. The fraction will have minutes in the numerator and seconds in the denominator:
\[ 230 , \text{seconds} \times \frac{1 , \text{minute}}{60 , \text{seconds}} \]
- Now we perform the multiplication:
\[ = \frac{230 , \text{minutes}}{60} \]
- Calculate the value:
\[ = \frac{230}{60} , \text{minutes} \]
Calculating \(230 \div 60\) gives:
\[ \approx 3.8333 , \text{minutes} \]
- We can round this to a more manageable number, if necessary:
\[ 3.83 , \text{minutes} \quad \text{(to two decimal places)} \]
Thus, \(230 , \text{seconds} \approx 3.83 , \text{minutes}\).
So the final answer is:
\[ \boxed{3.83 , \text{minutes}} \]