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1. Calculate 6.25×106−4.73×106%0D%0A6.25%0D%0A×%0D%0A10%0D%0A6%0D%0A−%0D%0A4.73%0D%0A×%0D%0A10%0D%0A6%0D%0A. Express your answer in scientific notation to 2 decimal places. (1 point)

2. The average distance from Earth to Mars is 2.25×108%0D%0A2.25%0D%0A×%0D%0A10%0D%0A8%0D%0A km, and the distance from Earth to Neptune is 4.3514×109%0D%0A4.3514%0D%0A×%0D%0A10%0D%0A9%0D%0A km. How much farther is Neptune from Earth than Mars? Express your answer in scientific notation. Do not round your answer.(1 point)%0D%0A km

3. Human hair grows at a rate of about 6.849×10−4%0D%0A6.849%0D%0A×%0D%0A10%0D%0A−%0D%0A4%0D%0A cm per hour to 2.329×10−2%0D%0A2.329%0D%0A×%0D%0A10%0D%0A−%0D%0A2%0D%0A cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation. Do not round your answer.(1 point)%0D%0A cm per hour%0D%0ACheck answer

4. Find 0.078−(5.2×10−3)%0D%0A0.078%0D%0A−%0D%0A(%0D%0A5.2%0D%0A×%0D%0A10%0D%0A−%0D%0A3%0D%0A)%0D%0A. Express your answer in scientific notation. Do not round your answer.(1 point)%0D%0A ×10−2

5. Earth’s radius is approximately 3,959 miles, while Jupiter’s radius is approximately 4.3441×104%0D%0A4.3441%0D%0A×%0D%0A10%0D%0A4%0D%0A miles. How much bigger is Jupiter’s radius compared to Earth’s? Express your answer in scientific notation. Do not round your answer.(1 point)%0D%0A ×%0D%0A×%0D%0A miles

9 answers

Let's solve each question step by step.

Question 1

Calculate \( 6.25 \times 10^6 - 4.73 \times 10^6 \).

  1. Both terms can be combined since they have the same power of 10: \[ (6.25 - 4.73) \times 10^6 = 1.52 \times 10^6 \]

  2. The answer is: \[ \text{Answer: } 1.52 \times 10^6 \]

Question 2

How much farther is Neptune ( \( 4.3514 \times 10^9 \) km ) from Earth than Mars ( \( 2.25 \times 10^8 \) km )?

  1. Convert the distances to the same power of ten for easy subtraction: \[ 2.25 \times 10^8 = 0.225 \times 10^9 \]

  2. Now subtract: \[ 4.3514 \times 10^9 - 0.225 \times 10^9 = (4.3514 - 0.225) \times 10^9 = 4.1264 \times 10^9 \]

  3. The answer is: \[ \text{Answer: } 4.1264 \times 10^9 \]

Question 3

Find the difference between the high end \( (2.329 \times 10^{-2}) \) and the low end \( (6.849 \times 10^{-4}) \).

  1. Convert the lower value to a common exponent for subtraction: \[ 6.849 \times 10^{-4} = 0.006849 \times 10^{-2} \]

  2. Now perform the subtraction: \[ 2.329 \times 10^{-2} - 0.006849 \times 10^{-2} = (2.329 - 0.006849) \times 10^{-2} = 2.322151 \times 10^{-2} \]

  3. The answer is: \[ \text{Answer: } 2.322151 \times 10^{-2} \]

Question 4

Calculate \( 0.078 - (5.2 \times 10^{-3}) \).

  1. First, convert \( 0.078 \) to scientific notation: \[ 0.078 = 7.8 \times 10^{-2} \]

  2. Now, perform the subtraction: \[ 7.8 \times 10^{-2} - 5.2 \times 10^{-3} = 7.8 \times 10^{-2} - 0.052 \times 10^{-2} = (7.8 - 0.052) \times 10^{-2} = 7.748 \times 10^{-2} \]

  3. The answer is: \[ \text{Answer: } 7.748 \times 10^{-2} \]

Question 5

Calculate how much bigger Jupiter’s radius \( (4.3441 \times 10^4) \) is compared to Earth’s radius \( (3959) \).

  1. First, convert \( 3959 \) to scientific notation: \[ 3959 \approx 3.959 \times 10^3 \]

  2. Now, calculate the difference: \[ 4.3441 \times 10^4 - 3.959 \times 10^3 = 4.3441 \times 10^4 - 0.3959 \times 10^4 = (4.3441 - 0.3959) \times 10^4 = 3.9482 \times 10^4 \]

  3. The answer is: \[ \text{Answer: } 3.9482 \times 10^4 \]

Summary of Answers:

  1. \( 1.52 \times 10^6 \)
  2. \( 4.1264 \times 10^9 \)
  3. \( 2.322151 \times 10^{-2} \)
  4. \( 7.748 \times 10^{-2} \)
  5. \( 3.9482 \times 10^4 \)
whats for 3 or 4? its not correct

Let’s carefully re-evaluate questions 3 and 4 again for correctness.

Question 3

Find the difference between the high end and the low end of the hair growth rate, \( 2.329 \times 10^{-2} \) cm/hr (high end) and \( 6.849 \times 10^{-4} \) cm/hr (low end).

  1. Subtract the low end from the high end: \[ 2.329 \times 10^{-2} - 6.849 \times 10^{-4} \]

  2. Convert \( 6.849 \times 10^{-4} \) to the same exponent as \( 2.329 \times 10^{-2} \): \[ 6.849 \times 10^{-4} = 0.06849 \times 10^{-2} \]

  3. Now subtract: \[ 2.329 \times 10^{-2} - 0.06849 \times 10^{-2} = (2.329 - 0.06849) \times 10^{-2} = 2.26051 \times 10^{-2} \]

So, the corrected answer for Question 3 is: \[ \text{Answer: } 2.26051 \times 10^{-2} \text{ cm/hr} \]

Question 4

Calculate \( 0.078 - (5.2 \times 10^{-3}) \).

  1. Convert \( 0.078 \) to scientific notation: \[ 0.078 = 7.8 \times 10^{-2} \]

  2. The operation now looks like this: \[ 7.8 \times 10^{-2} - 5.2 \times 10^{-3} \]

  3. Convert \( 5.2 \times 10^{-3} \) to the same exponent as \( 7.8 \times 10^{-2} \): \[ 5.2 \times 10^{-3} = 0.052 \times 10^{-2} \]

  4. Now subtract: \[ 7.8 \times 10^{-2} - 0.052 \times 10^{-2} = (7.8 - 0.052) \times 10^{-2} = 7.748 \times 10^{-2} \]

So, the answer for Question 4 is: \[ \text{Answer: } 7.748 \times 10^{-2} \]

Summary of Revised Answers:

  1. Question 3: \( 2.26051 \times 10^{-2} \) cm/hr
  2. Question 4: \( 7.748 \times 10^{-2} \)

If you require anything else or any further clarifications, please let me know!

change 4 PLEASE

Let’s reevaluate Question 4 step by step to ensure accuracy.

Question 4

Calculate \( 0.078 - (5.2 \times 10^{-3}) \).

  1. Convert \( 0.078 \) to scientific notation: \[ 0.078 = 7.8 \times 10^{-2} \]

  2. Now, subtract \( 5.2 \times 10^{-3} \): \[ 5.2 \times 10^{-3} = 0.052 \times 10^{-2} \] (This is done so both terms can be in the same exponent.)

  3. Perform the subtraction: \[ 7.8 \times 10^{-2} - 0.052 \times 10^{-2} = (7.8 - 0.052) \times 10^{-2} = 7.748 \times 10^{-2} \]

Now let’s express it in the form of scientific notation.

  1. Converting \( 7.748 \times 10^{-2} \) back to standard form: \[ 7.748 \times 10^{-2} = 0.07748 \]

Correct Final Answer:

The answer in scientific notation is \( 7.748 \times 10^{-2} \), which in standard form is \( 0.07748 \).

However, if the question requires us to express the answer in scientific notation multiplied by \( 10^{-2} \), we simply leave it as \( 7.748 \times 10^{-2} \) because it is already in that form.

If you were looking for a specific adjustment to the interpretation or structure of your answer, please clarify what you would like changed!

4 is 7.28

1. Subtract 4.66×10−5−7.34×10−7(1 point)%0D%0AResponses%0D%0A%0D%0A2.68×102%0D%0A2.68 times 10 squared%0D%0A%0D%0A−2.68×102%0D%0Anegative 2.68 times 10 squared%0D%0A%0D%0A4.5866×10−5%0D%0A4.5866 times 10 superscript negative 5 baseline%0D%0A%0D%0A−4.5866×10−5%0D%0Anegative 4.5866 times 10 superscript negative 5 baseline

2. The U.S. national debt was $2.9617×1013 in 2021 and $3.98×1011 in 1971. Find how much the debt increased in the 50-year period. (1 point)%0D%0AResponses%0D%0A%0D%0A$2.9219×1011%0D%0A2.9219 dollars times 10 superscript 11 baseline%0D%0A%0D%0A$1.0183×1024%0D%0A1.0183 dollars times 10 superscript 24 baseline%0D%0A%0D%0A$3.0015×1013%0D%0A3.0015 dollars times 10 superscript 13 baseline%0D%0A%0D%0A$2.9219×1013

3. The size of a hydrogen atom is about 1.2×10−10 m across. The size of an oxygen atom is 0.000000000152 m across. What is the difference between the sizes of these atoms in scientific notation?(1 point)%0D%0AResponses%0D%0A%0D%0A2.72×10−10 m%0D%0A2.72 times 10 superscript negative 10 baseline m%0D%0A%0D%0A3.2 ×10−10 m%0D%0A3.2 times 10 superscript negative 10 baseline m%0D%0A%0D%0A3.2×10−11 m%0D%0A3.2 times 10 superscript negative 11 baseline m%0D%0A%0D%0A3.2×10−9 m

4. Platelets and red blood cells are components of the blood. A typical platelet and red blood cell have diameters of approximately 2.33×10−6 m and 0.0000075 m, respectively. Which blood component has a bigger diameter, and approximately by how much?(1 point)%0D%0AResponses%0D%0A%0D%0AA red blood cell has a bigger diameter than a platelet by 5.17×10−6 m.%0D%0AA red blood cell has a bigger diameter than a platelet by 5.17 times 10 superscript negative 6 baseline m.%0D%0A%0D%0AA platelet has a bigger diameter than a red blood cell by 5.17×10−6 m.%0D%0AA platelet has a bigger diameter than a red blood cell by 5.17 times 10 superscript negative 6 baseline m.%0D%0A%0D%0AA red blood cell has a bigger diameter than a platelet by 9.83×10−6 m.%0D%0AA red blood cell has a bigger diameter than a platelet by 9.83 times 10 superscript negative 6 baseline m.%0D%0A%0D%0AA platelet has a bigger diameter than a red blood cell by 9.83×10−6 m.

5. China and India are the most populous countries in the world. China’s population is approximately 1.45×109, while India’s population is approximately 1,400,000,000. How many more people live in China than in India?(1 point)%0D%0AResponses%0D%0A%0D%0A5×109%0D%0A5 times 10 superscript 9 baseline%0D%0A%0D%0A5×1010%0D%0A5 times 10 superscript 10 baseline%0D%0A%0D%0A5×107%0D%0A5 times 10 superscript 7 baseline%0D%0A%0D%0A5×108

Let's work through each of your new questions step by step.

Question 1

Subtract \( 4.66 \times 10^{-5} - 7.34 \times 10^{-7} \).

  1. First, convert \( 7.34 \times 10^{-7} \) to the same exponent as \( 4.66 \times 10^{-5} \): \[ 7.34 \times 10^{-7} = 0.0000734 \times 10^{-5} \]

  2. Subtract: \[ 4.66 \times 10^{-5} - 0.0000734 \times 10^{-5} = (4.66 - 0.0734) \times 10^{-5} = 4.5866 \times 10^{-5} \]

Answer: \( 4.5866 \times 10^{-5} \)

Question 2

Find how much the U.S. national debt increased from $3.98 \times 10^{11}$ in 1971 to $2.9617 \times 10^{13}$ in 2021.

  1. Perform the subtraction: \[ 2.9617 \times 10^{13} - 3.98 \times 10^{11} \]

  2. Convert \( 3.98 \times 10^{11} \) to the same exponent as \( 2.9617 \times 10^{13} \): \[ 3.98 \times 10^{11} = 0.0398 \times 10^{13} \]

  3. Now subtract: \[ 2.9617 \times 10^{13} - 0.0398 \times 10^{13} = (2.9617 - 0.0398) \times 10^{13} = 2.9219 \times 10^{13} \]

Answer: \( 2.9219 \times 10^{13} \)

Question 3

Find the difference in size between a hydrogen atom (\( 1.2 \times 10^{-10} \) m) and an oxygen atom (0.000000000152 m or \( 1.52 \times 10^{-10} \) m).

  1. Subtract the two sizes: \[ 1.52 \times 10^{-10} - 1.2 \times 10^{-10} \]

  2. Perform the subtraction: \[ (1.52 - 1.2) \times 10^{-10} = 0.32 \times 10^{-10} \]

  3. Convert to scientific notation: \[ 0.32 \times 10^{-10} = 3.2 \times 10^{-11} \]

Answer: \( 3.2 \times 10^{-11} \) m

Question 4

Compare the diameters of platelets (\( 2.33 \times 10^{-6} \) m) and red blood cells (0.0000075 m or \( 7.5 \times 10^{-6} \) m).

  1. Find the difference between the two: \[ 7.5 \times 10^{-6} - 2.33 \times 10^{-6} \]

  2. Perform the subtraction: \[ (7.5 - 2.33) \times 10^{-6} = 5.17 \times 10^{-6} \]

Conclusion: A red blood cell has a bigger diameter than a platelet by \( 5.17 \times 10^{-6} \) m.

Answer: A red blood cell has a bigger diameter than a platelet by \( 5.17 \times 10^{-6} \) m.

Question 5

Find how many more people live in China (\( 1.45 \times 10^{9} \)) than in India, where India's population is \( 1,400,000,000 \) (or \( 1.4 \times 10^{9} \)).

  1. Subtract the populations: \[ 1.45 \times 10^{9} - 1.4 \times 10^{9} \]

  2. Perform the subtraction: \[ (1.45 - 1.4) \times 10^{9} = 0.05 \times 10^{9} \]

  3. Convert to scientific notation: \[ 0.05 \times 10^{9} = 5 \times 10^{7} \]

Answer: \( 5 \times 10^{7} \)

Summary of Final Answers:

  1. \( 4.5866 \times 10^{-5} \)
  2. \( 2.9219 \times 10^{13} \)
  3. \( 3.2 \times 10^{-11} \) m
  4. A red blood cell has a bigger diameter than a platelet by \( 5.17 \times 10^{-6} \) m
  5. \( 5 \times 10^{7} \)

If you have further questions or need assistance with anything else, feel free to ask!

PERFECT!!!

I'm glad to hear that you found the answers perfect! If you have any more questions or need further assistance, whether it's about scientific notation or any other topic, feel free to ask. Happy studying!

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