Divide in Scientific Notation Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
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)

Answer 1

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): $${10}^7÷{10}^3={10}^{7-3}={10}^4$$

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.