Convert 4.083×106

Question

kilometers to meters. Express the answer to the exact decimal place.

Note: 1 kilometer is equal to 1,000 meters.

(1 point)

Answer 1

To convert kilometers to meters, you multiply by 1,000 (since 1 kilometer is equal to 1,000 meters).

Given: \[ 4.083 \times 10^6 \text{ kilometers} \]

To convert to meters: \[ 4.083 \times 10^6 \text{ kilometers} \times 1,000 \text{ meters/kilometer} \]

This is the same as: \[ 4.083 \times 10^6 \times 10^3 \text{ meters} \]

Adding the exponents: \[ 4.083 \times 10^{6 + 3} \text{ meters} = 4.083 \times 10^9 \text{ meters} \]

Thus, the final answer is: \[ 4.083 \times 10^9 \text{ meters} \]

Answer 2

Ali’s farmhouse has a height of 2.307×108
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 3

To convert meters to centimeters, you multiply by 100 (since 1 meter is equal to 100 centimeters).

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

To convert to centimeters: \[ 2.307 \times 10^8 \text{ meters} \times 100 \text{ centimeters/meter} \]

This is the same as multiplying by \(10^2\) to account for the 100 centimeters in a meter: \[ 2.307 \times 10^8 \times 10^2 \text{ centimeters} \]

Adding the exponents: \[ 2.307 \times 10^{8 + 2} \text{ centimeters} = 2.307 \times 10^{10} \text{ centimeters} \]

Thus, the final answer in scientific notation is: \[ 2.307 \times 10^{10} \text{ centimeters} \]

Answer 4

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

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

Answer 5

To convert the dimensions from meters to millimeters, you multiply by 1,000 (since 1 meter is equal to 1,000 millimeters).

1. Convert the width:

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

To convert to millimeters: \[ 1.25 \times 10^{-8} \text{ meters} \times 1000 \text{ millimeters/meter} = 1.25 \times 10^{-8} \times 10^{3} \text{ millimeters} \]

Adding the exponents: \[ 1.25 \times 10^{-8 + 3} \text{ millimeters} = 1.25 \times 10^{-5} \text{ millimeters} \]

2. Convert the length:

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

To convert to millimeters: \[ 2.5 \times 10^{-6} \text{ meters} \times 1000 \text{ millimeters/meter} = 2.5 \times 10^{-6} \times 10^{3} \text{ millimeters} \]

Adding the exponents: \[ 2.5 \times 10^{-6 + 3} \text{ millimeters} = 2.5 \times 10^{-3} \text{ millimeters} \]

Final Dimensions:

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

So the dimensions of the sticky note in millimeters are:

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

Answer 6

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)

Answer 7

To find the total number of seconds for Jim's music library, we first need to calculate the total time in minutes and then convert that time into seconds.

Step 1: Calculate total time in minutes

Given:

• Number of songs = 1900
• Average time per song = 3.5 minutes

Total time in minutes: \[ \text{Total time} = \text{Number of songs} \times \text{Average time per song} = 1900 \times 3.5 \]

Calculating: \[ 1900 \times 3.5 = 6650 \text{ minutes} \]

Step 2: Convert total time to seconds

We know that 1 minute is equal to 60 seconds.

Total time in seconds: \[ 6650 \text{ minutes} \times 60 \text{ seconds/minute} = 399000 \text{ seconds} \]

Step 3: Express in scientific notation

To express \(399000\) in scientific notation:

\[ 399000 = 3.99 \times 10^5 \]

Final Answer

Thus, the total number of seconds the playlist will play is: \[ \boxed{3.99 \times 10^5 \text{ seconds}} \]