Divide in Scientific Notation Practice

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2 of 52 of 5 Items
Question
There are about 1.6×103
meters in a mile. About how many miles are there in 3.52×107
meters? Write your answer in scientific notation, expressed to the exact decimal place.(1 point)

1 answer

To find how many miles are in \( 3.52 \times 10^7 \) meters, we can set up the conversion using the given conversion factor of \( 1.6 \times 10^3 \) meters per mile:

\[ \text{Miles} = \frac{\text{Meters}}{\text{Meters per Mile}} = \frac{3.52 \times 10^7 \text{ meters}}{1.6 \times 10^3 \text{ meters/mile}} \]

Now, we can perform the division:

  1. Divide the coefficients (the numbers in front): \[ \frac{3.52}{1.6} = 2.2 \]

  2. Subtract the exponents (since we are dividing exponential terms): \[ 10^{7} \div 10^{3} = 10^{7-3} = 10^{4} \]

Putting it all together, we have:

\[ \text{Miles} = 2.2 \times 10^{4} \]

Thus, there are approximately \( 2.2 \times 10^4 \) miles in \( 3.52 \times 10^7 \) meters.