Ali’s farmhouse has a height of 2.307×10 to the power of 8

Question

meters. Convert the height to centimeters. Express your answer in scientific notation to the exact decimal place.

Note: 1 meter is equal to 100 centimeters.

Answer 1

To convert the height from meters to centimeters, you can use the conversion factor that 1 meter is equal to 100 centimeters.

Starting with the height in meters:

\[ 2.307 \times 10^8 \text{ meters} \]

Now, convert this to centimeters:

\[ 2.307 \times 10^8 \text{ meters} \times 100 \text{ cm/m} \]

This can be simplified as:

\[ 2.307 \times 10^8 \times 10^2 \text{ cm} \]

Because \(100\) can be expressed as \(10^2\):

\[ = 2.307 \times 10^{8 + 2} \text{ cm} \] \[ = 2.307 \times 10^{10} \text{ cm} \]

Thus, the height of Ali's farmhouse in centimeters expressed in scientific notation is:

\[ \boxed{2.307 \times 10^{10} \text{ cm}} \]

Answer 2

Kendra finds the dimensions of a sticky note. She uses a meter stick to determine that the dimensions are 1.25×10 to the power of−8 meters wide by 2.5×10 to the power of −6 meters long. Use scientific notation to write the dimensions in millimeters.

Note: 1 meter is equal to 1,000 millimeters.

Answer 3

To convert the dimensions from meters to millimeters, we use the conversion factor that 1 meter is equal to 1,000 millimeters (or \(10^3\) mm).

Step 1: Convert the width

The width is given as:

\[ 1.25 \times 10^{-8} \text{ meters} \]

To convert this to millimeters:

\[ 1.25 \times 10^{-8} \text{ meters} \times 1000 \text{ mm/m} \]

This simplifies to:

\[ 1.25 \times 10^{-8} \times 10^3 \text{ mm} \] \[ = 1.25 \times 10^{-8 + 3} \text{ mm} \] \[ = 1.25 \times 10^{-5} \text{ mm} \]

Step 2: Convert the length

The length is given as:

\[ 2.5 \times 10^{-6} \text{ meters} \]

To convert this to millimeters:

\[ 2.5 \times 10^{-6} \text{ meters} \times 1000 \text{ mm/m} \]

This simplifies to:

\[ 2.5 \times 10^{-6} \times 10^3 \text{ mm} \] \[ = 2.5 \times 10^{-6 + 3} \text{ mm} \] \[ = 2.5 \times 10^{-3} \text{ mm} \]

Final answer

Thus, the dimensions of the sticky note in millimeters are:

• Width: \(1.25 \times 10^{-5} \text{ mm}\)
• Length: \(2.5 \times 10^{-3} \text{ mm}\)

Expressing this together, Kendra's sticky note dimensions in scientific notation are:

\[ \text{Width: } \boxed{1.25 \times 10^{-5} \text{ mm}}, \quad \text{Length: } \boxed{2.5 \times 10^{-3} \text{ mm}} \]

Answer 4

Jim’s music library on his phone holds 1,900 songs. The songs have an average time of 3.5 minutes. Use scientific notation to find the total number of seconds the playlist will play. Express the answer to the exact decimal place.(1 point)
Responses

Answer 5

To find the total number of seconds that Jim's playlist will play, we need to multiply the number of songs by the average time of each song (in minutes) and then convert that time into seconds.

Step 1: Convert the average time from minutes to seconds

The average time per song is given as \(3.5\) minutes. To convert this into seconds, we use the conversion factor that \(1\) minute is equal to \(60\) seconds:

\[ 3.5 \text{ minutes} = 3.5 \times 60 \text{ seconds} \]

Calculating this gives:

\[ 3.5 \times 60 = 210 \text{ seconds} \]

Step 2: Calculate the total time for all songs

Now, we multiply the total number of songs, which is \(1,900\), by the time per song in seconds:

\[ \text{Total time} = 1,900 \text{ songs} \times 210 \text{ seconds/song} \]

Calculating this:

\[ 1,900 \times 210 = 399,000 \text{ seconds} \]

Step 3: Convert the total time into scientific notation

To express \(399,000\) in scientific notation, we can rewrite it as:

\[ 3.99 \times 10^5 \text{ seconds} \]

Final Answer

Thus, the total number of seconds the playlist will play, expressed in scientific notation to the exact decimal place, is:

\[ \boxed{3.99 \times 10^5 \text{ seconds}} \]

Answer 6

In chemistry class, Carlos calculated the number of molecules in 100 moles. The calculator displayed the number 6.02E25. What is the number of molecules in 100 moles in scientific notation?(1 point)

Answer 7

To find the number of molecules in 100 moles, we start with the known Avogadro's number, which is approximately \(6.02 \times 10^{23}\) molecules per mole.

To calculate the number of molecules in 100 moles, we can use the following formula:

\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]

Substituting in the values:

\[ \text{Number of molecules} = 100 \text{ moles} \times 6.02 \times 10^{23} \text{ molecules/mole} \]

Calculating this gives:

\[ = 100 \times 6.02 \times 10^{23} \] \[ = 6.02 \times 10^{25} \text{ molecules} \]

Therefore, the number of molecules in 100 moles, expressed in scientific notation, is:

\[ \boxed{6.02 \times 10^{25} \text{ molecules}} \]