There are about 1.6×10^3 meters in a mile. About how many miles are there in 3.52×10^3 meters? Write your answer in scientific notation, expressed to the exact decimal place.

Answer 1

To convert meters to miles using the conversion factor \(1.6 \times 10^3\) meters per mile, you can set up the following calculation:

\[ \text{miles} = \frac{\text{meters}}{\text{meters per mile}} = \frac{3.52 \times 10^3 \text{ meters}}{1.6 \times 10^3 \text{ meters per mile}} \]

Now we can perform the division:

\[ \text{miles} = \frac{3.52}{1.6} \times \frac{10^3}{10^3} \]

The \(10^3\) meters units cancel out:

\[ \text{miles} = \frac{3.52}{1.6} \]

Calculating \(\frac{3.52}{1.6}\):

\[ \frac{3.52}{1.6} = 2.2 \]

Therefore, we have:

\[ \text{miles} = 2.2 \times 10^0 \]

Now expressing \(2.2\) in scientific notation gives us:

\[ 2.2 \times 10^0 \]

Thus, the final answer is:

\[ \boxed{2.2 \times 10^0} \]

Answer 2

that is not correct

Answer 3

Let's redo the calculation to find out how many miles are in \(3.52 \times 10^3\) meters, using the conversion factor of \(1.6 \times 10^3\) meters per mile.

To convert meters to miles, we divide the number of meters by the number of meters in a mile:

\[ \text{miles} = \frac{3.52 \times 10^3 \text{ meters}}{1.6 \times 10^3 \text{ meters per mile}} \]

Now, we calculate that:

\[ \text{miles} = \frac{3.52}{1.6} \times \frac{10^3}{10^3} \]

The \(10^3\) terms cancel out:

\[ \text{miles} = \frac{3.52}{1.6} \]

Calculating \(\frac{3.52}{1.6}\):

\[ 3.52 \div 1.6 = 2.2 \]

Thus,

\[ \text{miles} = 2.2 \]

Now we should express \(2.2\) in scientific notation. It can be written as:

\[ 2.2 \times 10^0 \]

However, let’s ensure that we performed the conversion from meters correctly:

To calculate miles per meter, we can also express it directly:

\[ 1 \text{ mile} = 1600 \text{ meters} = 1.6 \times 10^3 \text{ meters} \]

To convert \(3.52 \times 10^3\) meters to miles:

\[ \text{miles} = \frac{3.52 \times 10^3}{1.6 \times 10^3} = \frac{3.52}{1.6} \]

Calculating \(\frac{3.52}{1.6}\) yields:

\[ 3.52 \div 1.6 = 2.2 \]

Apologies for any confusion in the earlier explanation. The proper number of miles in scientific notation is \(2.20 \times 10^0\) to two decimal places.

So the answer is:

\[ \boxed{2.20 \times 10^0} \]

Thank you for your patience.