An asteroid is heading towards mars at the rate of 7.7 x 10^4 mi./hr. If the asteroid is 3.311 x 10^8 miles away from mars, how many hours will it be before it hits mars? Write the answer in scientific notation, expressed to the exact decimal place

Answer 1

To determine how many hours it will take for the asteroid to hit Mars, we need to divide the distance to Mars by the speed of the asteroid.

The distance to Mars is: \[ 3.311 \times 10^8 \text{ miles} \]

The speed of the asteroid is: \[ 7.7 \times 10^4 \text{ miles per hour} \]

We calculate the time \( t \) in hours using the formula: \[ t = \frac{\text{distance}}{\text{speed}} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ miles/hour}} \]

Now we perform the division:

1. Divide the coefficients: \[ \frac{3.311}{7.7} \approx 0.430 \]

2. Subtract the exponents: \[ 10^8 \div 10^4 = 10^{8-4} = 10^4 \]

Putting it all together: \[ t \approx 0.430 \times 10^4 \]

To express this in proper scientific notation, convert \( 0.430 \) to \( 4.30 \) and decrease the exponent: \[ 0.430 \times 10^4 = 4.30 \times 10^3 \]

Thus, the time before the asteroid hits Mars is: \[ \boxed{4.30 \times 10^3} \text{ hours} \]

Answer 2

A field of 3.9 mi^2 is it being subdivided into 1.3 x 10^3 family Gardens. How many square miles will there be in each garden? write the answer in scientific notation.

Answer 3

To find the area that each garden will have, we need to divide the total area of the field by the number of family gardens.

1. The total area of the field is: \[ 3.9 \text{ mi}^2 \]

2. The number of family gardens is: \[ 1.3 \times 10^3 \]

Now, we can calculate the area for each garden using the formula: \[ \text{Area per garden} = \frac{\text{Total area}}{\text{Number of gardens}} = \frac{3.9}{1.3 \times 10^3} \]

3. First, let's calculate the division of the coefficients: \[ \frac{3.9}{1.3} \approx 3.0 \quad (\text{keeping one decimal for now}) \]

4. Now, for the powers of ten, we can consider: \[ \frac{1}{10^3} = 10^{-3} \]

5. Combining these, we have: \[ \text{Area per garden} \approx 3.0 \times 10^{-3} \text{ mi}^2 \]

To express this in proper scientific notation, we can write \( 3.0 \) as \( 3.00 \) to keep two decimal places consistent: \[ 3.0 \times 10^{-3} = 3.00 \times 10^{-3} \]

Thus, the area of each family garden is: \[ \boxed{3.00 \times 10^{-3}} \text{ mi}^2 \]