Question

Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.

How many minutes are in 230 seconds

Answer 1

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:

1. Start with the given quantity in seconds:

\[
230 \, \text{seconds}
\]

2. 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:

\[
230 \, \text{seconds} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}}
\]

3. Now we perform the multiplication:

\[
= \frac{230 \, \text{minutes}}{60}
\]

4. Calculate the value:

\[
= \frac{230}{60} \, \text{minutes}
\]

Calculating \(230 \div 60\) gives:

\[
\approx 3.8333 \, \text{minutes}
\]

5. 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:

\[
\boxed{3.83 \, \text{minutes}}
\]