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:

$${10}^8÷{10}^4={10}^{8-4}={10}^4$$

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:

$$\boxed{{\displaystyle 4.30\times {10}^3}}\text{ hours}$$

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:

$$\boxed{{\displaystyle 3.0\times {10}^{-3}}},{\text{mi}}^2$$

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.