An asteriod is heading toward 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 find the time it takes for the asteroid to hit Mars, we can use the formula:

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

Given:

• Distance = \(3.311 \times 10^8\) miles
• Speed = \(7.7 \times 10^4\) miles/hour

Now, we substitute the 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 in scientific notation, we divide the coefficients and subtract the exponents:

1. Divide the coefficients:

\[ \frac{3.311}{7.7} \approx 0.430 \]

2. Calculate the exponents:

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

Putting it all together, we have:

\[ \text{Time} \approx 0.430 \times 10^4 \]

To express this in proper scientific notation, we adjust \(0.430\) to \(4.30\) and decrease the exponent by 1:

\[ 4.30 \times 10^3 \text{ hours} \]

Therefore, the asteroid will hit Mars in approximately:

\[ \boxed{4.30 \times 10^3} \text{ hours} \]

Answer 2

A field of 3.9 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.

Answer 3

To find the area of each family garden, we can use the formula:

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

Given:

• Total area = \(3.9 , \text{mi}^2\)
• Number of gardens = \(1.3 \times 10^3\)

Substituting the values into the formula:

\[ \text{Area per garden} = \frac{3.9 , \text{mi}^2}{1.3 \times 10^3} \]

Now, let's perform the division:

1. Divide the coefficients:

\[ \frac{3.9}{1.3} \approx 3.0 \]

2. For the exponents, we can express \(3.9\) in scientific notation as \(3.9 \times 10^0\):

\[ \text{Area per garden} = \frac{3.9 \times 10^0}{1.3 \times 10^3} = \frac{3.9}{1.3} \times 10^{0-3} = 3.0 \times 10^{-3} \]

Thus, the area per garden is:

\[ \text{Area per garden} = 3.0 \times 10^{-3} , \text{mi}^2 \]

Therefore, the area of each family garden in scientific notation is:

\[ \boxed{3.0 \times 10^{-3}} , \text{mi}^2 \]

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.

Answer 5

The notation \(1.78E12\) is a way of representing numbers in scientific notation, which is often used for very large or very small numbers. In this format:

• \(E\) can be thought of as "times ten raised to the power of".
• The number before the \(E\) is the coefficient.
• The number after the \(E\) is the exponent of 10.

So, \(1.78E12\) means:

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

To interpret what this means in a more standard format, you can multiply \(1.78\) by \(10^{12}\):

\[ 1.78 \times 10^{12} = 1,780,000,000,000 \]

This is a 1 followed by 12 zeros.

Therefore, \(1.78E12\) represents the value 1 trillion, 780 billion.

In summary, \(1.78E12\) indicates that the product of the two large numbers Charlee is calculating is \(1.78 \times 10^{12}\), or 1,780,000,000,000 in standard decimal notation.