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An asteroid is heading toward Mars at the rate of 7.7×104

mi./hr. If the asteroid is 3.311×108
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.(1 point)
hours

5 answers

To find out how many hours it will take for the asteroid to hit Mars, we can use the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Given that the distance to Mars is \(3.311 \times 10^8\) miles and the speed of the asteroid is \(7.7 \times 10^4\) miles per hour, we can substitute these values into the formula:

\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ mi/hr}} \]

Now, we perform the division:

  1. Dividing the coefficients:

\[ \frac{3.311}{7.7} \approx 0.4303 \]

  1. Subtracting the exponents (as per the rules of scientific notation):

\[ 10^{8 - 4} = 10^4 \]

Thus, we have:

\[ \text{Time} \approx 0.4303 \times 10^4 \]

To express \(0.4303 \times 10^4\) in proper scientific notation, we convert \(0.4303\) to \(4.303\) and reduce the exponent by 1:

\[ \text{Time} \approx 4.303 \times 10^3 \text{ hours} \]

Therefore, the final answer in scientific notation, expressed to the exact decimal place, is:

\[ \boxed{4.303 \times 10^3} \]

whats the answer

To find the time it takes for the asteroid to hit Mars, we will calculate it step by step.

Given:

  • Distance to Mars: \(3.311 \times 10^8\) miles
  • Speed of the asteroid: \(7.7 \times 10^4\) miles per hour

Using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Substituting the given values:

\[ \text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ mi/hr}} \]

Now let's do the calculation:

  1. Divide the coefficients:

\[ \frac{3.311}{7.7} \approx 0.4303 \]

  1. Subtract the exponents:

The exponent for distance is \(10^8\) and the exponent for speed is \(10^4\):

\[ 10^{8-4} = 10^4 \]

Putting this together:

\[ \text{Time} = 0.4303 \times 10^4 \]

Now we convert \(0.4303\) into scientific notation:

\[ 0.4303 \times 10^4 = 4.303 \times 10^3 \]

Thus, the time it will take for the asteroid to hit Mars is:

\[ \boxed{4.303 \times 10^3} \text{ hours} \]

This is approximately 4303 hours.

i though it was 4,3 x 10^3

The correct representation in scientific notation should include the proper number of significant figures based on the precision of the original values.

The calculation results in:

\[ \text{Time} = 4.303 \times 10^3 \text{ hours} \]

If you prefer rounding it to one decimal place, where appropriate for simplicity in notation, it would indeed be:

\[ 4.3 \times 10^3 \text{ hours} \]

So, if you are looking for that more rounded representation, the answer can be expressed as:

\[ \boxed{4.3 \times 10^3} \text{ hours} \]

However, the precise answer from the calculations provided earlier is \(4.303 \times 10^3\) hours. If the focus is on significant figures or rounding, \(4.3 \times 10^3\) is also acceptable. Thank you for your clarification!