1. Convert 3.875×109%0D%0A3.875%0D%0A×%0D%0A10%0D%0A9%0D%0A meters to kilometers. Express the answer to the exact decimal place.%0D%0A%0D%0ANote: 1 kilometer is equal to 1,000 meters.%0D%0A%0D%0A(1 point)%0D%0A km

Question

2. Convert 4.083×106%0D%0A4.083%0D%0A×%0D%0A10%0D%0A6%0D%0A kilometers to meters. Express the answer to the exact decimal place.%0D%0A%0D%0ANote: 1 kilometer is equal to 1,000 meters.%0D%0A%0D%0A(1 point)%0D%0A meters

3. Ali’s farmhouse has a height of 2.307×108%0D%0A2.307%0D%0A×%0D%0A10%0D%0A8%0D%0A meters. Convert the height to centimeters. Express your answer in scientific notation to the exact decimal place.%0D%0A%0D%0ANote: 1 meter is equal to 100 centimeters.%0D%0A%0D%0A(1 point)%0D%0A centimeters

4. Alberto added two very small numbers using a calculator. The calculator displayed the number 6.13E−14%0D%0A6.13%0D%0AE%0D%0A−%0D%0A14%0D%0A. What is this number in scientific notation?(1 point)%0D%0A×10−14

5. Dina computed the mass of 1,000 protons in grams. The calculator displayed the number 1.67E−21%0D%0A1.67%0D%0AE%0D%0A−%0D%0A21%0D%0A. What is the mass of 1,000 protons in scientific notation?(1 point)%0D%0A1.67 ×%0D%0A1.67%0D%0A %0D%0A×%0D%0A grams

Answer 1

Let's go through each of your questions step-by-step.

1. Convert \(3.875 \times 10^9\) meters to kilometers.

   • Since \(1 \text{ kilometer} = 1,000 \text{ meters}\), we can convert by dividing by 1,000. \[ \frac{3.875 \times 10^9 \text{ meters}}{1,000} = 3.875 \times 10^6 \text{ kilometers} \]
   • Answer: \(3.875 \times 10^6\) km

2. Convert \(4.083 \times 10^6\) kilometers to meters.

   • Multiply by 1,000 to convert kilometers to meters. \[ 4.083 \times 10^6 \text{ kilometers} \times 1,000 = 4.083 \times 10^9 \text{ meters} \]
   • Answer: \(4.083 \times 10^9\) meters

3. Convert \(2.307 \times 10^8\) meters to centimeters.

   • Since \(1 \text{ meter} = 100 \text{ centimeters}\), multiply by 100 (or \(10^2\)). \[ 2.307 \times 10^8 \text{ meters} \times 100 = 2.307 \times 10^{10} \text{ centimeters} \]
   • Answer: \(2.307 \times 10^{10}\) centimeters

4. Convert \(6.13E−14\) to scientific notation.

   • The notation \(6.13E−14\) is already in scientific notation.
   • Answer: \(6.13 \times 10^{-14}\)

5. Convert \(1.67E−21\) to scientific notation.

   • The notation \(1.67E−21\) is already in scientific notation.
   • Answer: \(1.67 \times 10^{-21}\) grams

Here are all the answers summarized:

1. \(3.875 \times 10^6\) km
2. \(4.083 \times 10^9\) meters
3. \(2.307 \times 10^{10}\) centimeters
4. \(6.13 \times 10^{-14}\)
5. \(1.67 \times 10^{-21}\) grams

Answer 2

YES!!!

1. 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.%0D%0A%0D%0ANote: 1 meter is equal to 1,000 millimeters.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A1.25×10−10 by 2.5×10−8 millimeters%0D%0A 1.25 times 10 superscript negative 10 baseline by 2.5 times 10 superscript negative 8 baseline millimeters%0D%0A%0D%0A1.25×10−5 by 2.5×10−3 millimeters%0D%0A1.25 times 10 superscript negative 5 baseline by 2.5 times 10 negative cubed millimeters%0D%0A%0D%0A1.25×10−11 by 2.5×10−9 millimeters%0D%0A1.25 times 10 superscript negative 11 baseline by 2.5 times 10 superscript negative 9 baseline millimeters%0D%0A%0D%0A1.25×10−6 by 2.5×10−4 millimeters

2. 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)%0D%0AResponses%0D%0A%0D%0A3.99×104 seconds%0D%0A3.99 times 10 superscript 4 baseline seconds%0D%0A%0D%0A3.99×103 seconds%0D%0A3.99 times 10 cubed seconds%0D%0A%0D%0A0.399×106 seconds%0D%0A0.399 times 10 superscript 6 baseline seconds%0D%0A%0D%0A3.99×105 seconds

3. 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)%0D%0AResponses%0D%0A%0D%0A25×106.02%0D%0A25 times 10 superscript 6.02 baseline%0D%0A%0D%0A6.02×25%0D%0A6.02 times 25%0D%0A%0D%0A6.02×1025%0D%0A6.02 times 10 superscript 25 baseline%0D%0A%0D%0A6.02+1025

4. In government class, Nadia computed the amount of debt of the federal government after a third of it was paid in 1995. The calculator displayed the number 3.28E12. What is this number in scientific notation?(1 point)%0D%0AResponses%0D%0A%0D%0A3.28+1012%0D%0A3.28 plus 10 superscript 12 baseline%0D%0A%0D%0A12×103.28%0D%0A12 times 10 superscript 3.28 baseline%0D%0A%0D%0A3.28×1012%0D%0A3.28 times 10 superscript 12 baseline%0D%0A%0D%0A3.28×10−12

5. Sam is comparing the half-life of two isotopes of uranium. The half-life of Uranium-238 is 4.5×109 years. The half-life of Uranium-233 is 1.6×105 years. He computed how much greater the half-life of Uranium-238 is than that of Uranium-233, and his calculator displayed the number 2.81E4. What is this number in scientific notation?(1 point)%0D%0AResponses%0D%0A%0D%0A2.81×10−4%0D%0A2.81 times 10 superscript negative 4 baseline%0D%0A%0D%0A4×102.81%0D%0A4 times 10 superscript 2.81 baseline%0D%0A%0D%0A2.81×104%0D%0A2.81 times 10 superscript 4 baseline%0D%0A%0D%0A2.81+104

Answer 3

Let's break down each of the questions step-by-step:

1. Convert the dimensions of the sticky note from meters to millimeters.

   • The dimensions given are \(1.25 \times 10^{-8}\) meters wide and \(2.5 \times 10^{-6}\) meters long.
   • To convert from meters to millimeters, multiply by 1,000 (or \(10^3\)).
   • For width: \[ 1.25 \times 10^{-8} \text{ m} \times 1,000 = 1.25 \times 10^{-8} \times 10^3 = 1.25 \times 10^{-5} \text{ mm} \]
   • For length: \[ 2.5 \times 10^{-6} \text{ m} \times 1,000 = 2.5 \times 10^{-6} \times 10^3 = 2.5 \times 10^{-3} \text{ mm} \]
   • Answer: \(1.25 \times 10^{-5} \text{ by } 2.5 \times 10^{-3}\) millimeters

2. Calculate the total number of seconds for Jim’s music library.

   • Jim has 1,900 songs with an average time of 3.5 minutes per song.
   • First, convert minutes to seconds: \(3.5 \text{ minutes} \times 60 \text{ seconds/minute} = 210 \text{ seconds}\).
   • Now, multiply by the number of songs: \[ 1,900 \text{ songs} \times 210 \text{ seconds/song} = 399,000 \text{ seconds} \]
   • In scientific notation: \[ 399,000 = 3.99 \times 10^5 \text{ seconds} \]
   • Answer: \(3.99 \times 10^5\) seconds

3. Determine the number of molecules in 100 moles.

   • Carlos’s calculator shows \(6.02E25\) molecules, which is the same as \(6.02 \times 10^{25}\).
   • Answer: \(6.02 \times 10^{25}\)

4. Convert the amount of federal government debt from scientific notation.

   • \(3.28E12\) is in scientific notation, which is already expressed as \(3.28 \times 10^{12}\).
   • Answer: \(3.28 \times 10^{12}\)

5. Express Sam's calculation of the difference in half-lives of the isotopes.

   • The calculator shows \(2.81E4\), which is \(2.81 \times 10^4\).
   • Answer: \(2.81 \times 10^{4}\)

Here are all the answers summarized:

1. \(1.25 \times 10^{-5}\) by \(2.5 \times 10^{-3}\) millimeters
2. \(3.99 \times 10^5\) seconds
3. \(6.02 \times 10^{25}\)
4. \(3.28 \times 10^{12}\)
5. \(2.81 \times 10^{4}\)

Answer 4

100!!

Answer 5

I'm glad to hear that you found the answers helpful! If you have any more questions or need further assistance with anything else, feel free to ask. Happy studying! 😊