An asteroid is heading toward Marts 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.

Question

__ Hours

Answer 1

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

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

Given:

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

We can substitute these values into the formula:

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

To perform the division, we first divide the coefficients:

\[ \frac{3.311}{7.7} \approx 0.4300 \]

Next, we divide the powers of 10:

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

Now, combining both results:

\[ \text{Time} \approx 0.4300 \times 10^4 \]

This can be written in scientific notation:

\[ 4.300 \times 10^3 \text{ hours} \]

Thus, the time before the asteroid hits Mars is:

\[ \boxed{4.300 \times 10^3} \]

Answer 2

A field of 3.8 mi^2 is 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.
_mi^2

Answer 3

To find out how many square miles will be in each family garden, you can use the formula:

\[ \text{Area per garden} = \frac{\text{Total area}}{\text{Number of gardens}} \]

Given:

• Total area of the field = \(3.8 \text{ mi}^2\)
• Number of family gardens = \(1.3 \times 10^3\)

Now, substituting the values into the formula:

\[ \text{Area per garden} = \frac{3.8 \text{ mi}^2}{1.3 \times 10^3} \]

To perform the division, we first divide the coefficients:

\[ \frac{3.8}{1.3} \approx 2.92307692 \]

Next, we divide the powers of 10. The denominator \(1.3 \times 10^3\) can be treated as \(1.3 \times 10^3\) which gives us:

\[ \text{Area per garden} \approx \frac{2.92307692}{1} \times \frac{1}{10^3} \]

Thus converting to scientific notation:

\[ 2.92307692 \div 10^3 = 2.92307692 \times 10^{-3} \]

Finally, rounding to three significant figures:

\[ \approx 2.92 \times 10^{-3} \]

Thus, the area per garden is:

\[ \boxed{2.92 \times 10^{-3}} \text{ mi}^2 \]

Answer 4

Charlee is using her calculator to find the product of two large numbers. Her calculator shows 1.78E12
on the display. Interpret what this means. (2 points)

Answer 5

The notation "1.78E12" is a way to represent numbers in scientific notation, which is commonly used for large or small numbers. In this case, "1.78E12" means:

\[ 1.78 \times 10^{12} \]

This indicates that the number is 1.78 multiplied by 10 raised to the 12th power.

To interpret this:

• The number 10^12 is equal to 1,000,000,000,000 (one trillion).
• Therefore, \(1.78 \times 10^{12}\) equals 1.78 trillion.

In summary, Charlee’s calculator is displaying a product of two large numbers that equals 1.78 trillion.

Answer 6

The notation 1.78E12 is a way to show numbers in a scientific notation, often used for large or small numbers. The first set of numbers "1.78" is the number that will be multiplied, while the letter "E" is used to represent "10 times power" of the last number set "12", which is the exponent that the first number set will be multiplied by. In this case, Charlee's calculator displaying 1.78E12 means 1.78 X 10^12, equaling 1.78 trillion.

Is this correct?

Answer 7

Yes, your explanation is correct!

You clearly explained the format of scientific notation:

• "1.78" is the coefficient that will be multiplied.
• "E" represents "times 10 to the power of," which is a common notation in calculators and programming.
• "12" is the exponent, indicating how many times to multiply the coefficient by 10.

Thus, "1.78E12" is equivalent to \(1.78 \times 10^{12}\). Conclusively, this equals 1.78 trillion (since \(10^{12}\) is equal to 1,000,000,000,000).

Your interpretation is accurate and clearly conveys what the notation means. Well done!