Ask a New Question
Menu

1. For what value of a%0D%0A𝑎%0D%0A will 8×103%0D%0A8%0D%0A×%0D%0A10%0D%0A3%0D%0A be 40 times larger than a×102%0D%0A𝑎%0D%0A×%0D%0A10%0D%0A2%0D%0A?(1 point)

2. One second is approximately 0.0000115741 of a day. What is this number in scientific notation?(1 point)

3. The temperature of the sun at its center is about 2.7×107%0D%0A2.7%0D%0A×%0D%0A10%0D%0A7%0D%0A degrees Fahrenheit. What is this temperature written in decimal notation?(1 point)%0D%0A degrees Fahrenheit

4. Use scientific notation to determine which of these numbers has the least value: 98,789,000; 987,890,000; or 89,987,000. Write your answer in scientific notation, expressed to the exact decimal place.(1 point)

5. Place the numbers in descending order.%0D%0A%0D%0A2.3 × 10−10%0D%0A2.3%0D%0A %0D%0A×%0D%0A %0D%0A10%0D%0A−%0D%0A10%0D%0A; 3.2 × 10−10%0D%0A3.2%0D%0A %0D%0A×%0D%0A %0D%0A10%0D%0A−%0D%0A10%0D%0A; 2.3 × 10−12%0D%0A2.3%0D%0A %0D%0A×%0D%0A %0D%0A10%0D%0A−%0D%0A12%0D%0A; 2.3 × 10−8%0D%0A2.3%0D%0A %0D%0A×%0D%0A %0D%0A10%0D%0A−%0D%0A8%0D%0A%0D%0A(2 points)%0D%0A; ; ;

6. Janiya is taking a road trip. The distance she plans to travel can be written as 3×102%0D%0A3%0D%0A×%0D%0A10%0D%0A2%0D%0A kilometers, 3×105%0D%0A3%0D%0A×%0D%0A10%0D%0A5%0D%0A meters, 3×107%0D%0A3%0D%0A×%0D%0A10%0D%0A7%0D%0A centimeters, or 3×108%0D%0A3%0D%0A×%0D%0A10%0D%0A8%0D%0A millimeters. Which distance uses the most appropriate units?(1 point)%0D%0AResponses%0D%0A%0D%0A3×108%0D%0A3%0D%0A×%0D%0A10%0D%0A8%0D%0A millimeters%0D%0A3 times 10 to the 8th power millimeters%0D%0A%0D%0A3×105%0D%0A3%0D%0A×%0D%0A10%0D%0A5%0D%0A meters%0D%0A3 times 10 to the 5th power meters%0D%0A%0D%0A3×102%0D%0A3%0D%0A×%0D%0A10%0D%0A2%0D%0A kilometers%0D%0A3 times 10 squared kilometers%0D%0A%0D%0A3×107%0D%0A3%0D%0A×%0D%0A10%0D%0A7%0D%0A centimeters

7. A national park covers an area of 1.42×106%0D%0A1.42%0D%0A×%0D%0A10%0D%0A6%0D%0A acres. A nearby national forest covers an area of 1.2×106%0D%0A1.2%0D%0A×%0D%0A10%0D%0A6%0D%0Aacres. What is the total number of acres in the park and the forest combined?(1 point)%0D%0AResponses%0D%0A%0D%0A2.62×106%0D%0A2.62%0D%0A×%0D%0A10%0D%0A6%0D%0A2.62 times 10 superscript 6 baseline%0D%0A%0D%0A2.62×1012%0D%0A2.62%0D%0A×%0D%0A10%0D%0A12%0D%0A2.62 times 10 superscript 12 baseline%0D%0A%0D%0A1.54×106%0D%0A1.54%0D%0A×%0D%0A10%0D%0A6%0D%0A1.54 times 10 superscript 6 baseline%0D%0A%0D%0A15.5×106

8. The distance from Venus to the sun is about 67,000,000 miles. The distance from Earth to the sun is about 2.6×107%0D%0A2.6%0D%0A×%0D%0A10%0D%0A7%0D%0A farther. What is the distance from Earth to the sun? Write your answer in scientific notation to 1 decimal place.(1 point)%0D%0A×107%0D%0A×%0D%0A10%0D%0A7%0D%0A miles

9. Calculate 4.8×10−3−9.4×10−6%0D%0A4.8%0D%0A×%0D%0A10%0D%0A−%0D%0A3%0D%0A−%0D%0A9.4%0D%0A×%0D%0A10%0D%0A−%0D%0A6%0D%0A . Express the answer in scientific notation rounding to 2 decimal places.(1 point)

10. A strand of hair has an average mass of 2.17×10−5%0D%0A2.17%0D%0A×%0D%0A10%0D%0A−%0D%0A5%0D%0A ounces. A grain of rice has an average mass of 0.002 ounces. How much heavier is a grain of rice than a strand of hair? Express your answer in scientific notation.(1 point)%0D%0A ×%0D%0A×%0D%0A ounces

7 answers

Sure! Let's go through each of these problems step by step.

  1. Problem 1: For what value of \( a \) will \( 8 \times 10^3 \) be 40 times larger than \( a \times 10^2 \)?

    We want: \[ 8 \times 10^3 = 40 \times (a \times 10^2) \] Simplifying gives: \[ 8 \times 10^3 = 40a \times 10^2 \] Dividing both sides by \( 10^2 \): \[ 8 \times 10 = 40a \] \[ 80 = 40a \] Solving for \( a \): \[ a = \frac{80}{40} = 2 \]

  2. Problem 2: What is 0.0000115741 in scientific notation?

    This can be expressed as: \[ 1.15741 \times 10^{-5} \]

  3. Problem 3: What is \( 2.7 \times 10^7 \) in decimal notation?

    This is: \[ 27,000,000 \text{ degrees Fahrenheit} \]

  4. Problem 4: Use scientific notation to determine which of these numbers has the least value: \( 98,789,000; 987,890,000; \) or \( 89,987,000 \).

    • \( 98,789,000 = 9.8789 \times 10^7 \)
    • \( 987,890,000 = 9.8789 \times 10^8 \)
    • \( 89,987,000 = 8.9987 \times 10^7 \)

    The least value is \( 8.9987 \times 10^7 \).

  5. Problem 5: Place the numbers in descending order.

    • \( 2.3 \times 10^{-8} = 0.000000023 \)
    • \( 2.3 \times 10^{-10} = 0.000000000023 \)
    • \( 3.2 \times 10^{-10} = 0.000000000032 \)
    • \( 2.3 \times 10^{-12} = 0.000000000000023 \)

    In descending order:

    • \( 2.3 \times 10^{-8} \)
    • \( 3.2 \times 10^{-10} \)
    • \( 2.3 \times 10^{-10} \)
    • \( 2.3 \times 10^{-12} \)

  6. Problem 6: Which distance uses the most appropriate units?

    • \( 3 \times 10^2 \) kilometers = 300 kilometers
    • \( 3 \times 10^5 \) meters = 300,000 meters
    • \( 3 \times 10^7 \) centimeters = 30,000,000 centimeters
    • \( 3 \times 10^8 \) millimeters = 300,000,000 millimeters

    The most appropriate unit for a distance would be kilometers, given that the other units express significantly larger values.

  7. Problem 7: What is the total number of acres in the park and the forest combined?

    \[ 1.42 \times 10^6 + 1.2 \times 10^6 = (1.42 + 1.2) \times 10^6 = 2.62 \times 10^6 \text{ acres} \]

  8. Problem 8: What is the distance from Earth to the sun?

    The distance from Venus to the sun is \( 6.7 \times 10^7 \) miles. The distance from Venus to the Earth is \( 2.6 \times 10^7 \).

    Thus: \[ \text{Distance from Earth to the sun} = 6.7 \times 10^7 + 2.6 \times 10^7 = (6.7 + 2.6) \times 10^7 = 9.3 \times 10^7 \]

  9. Problem 9: Calculate \( 4.8 \times 10^{-3} - 9.4 \times 10^{-6} \).

    Converting to scientific notation: \[ 4.8 \times 10^{-3} = 4.8 \times 10^{-3} \] Converting \( 9.4 \times 10^{-6} \): \[ 9.4 \times 10^{-6} = 0.0000094 \]

    To perform the subtraction, convert \( 4.8 \times 10^{-3} \) to the same power: \[ 4.8 \times 10^{-3} = 4800 \times 10^{-6} \] Now subtract: \[ 4800 \times 10^{-6} - 9.4 \times 10^{-6} = (4800 - 9.4) \times 10^{-6} = 4790.6 \times 10^{-6} \] Converting back to scientific notation: \[ 4.7906 \times 10^{-3} \]

  10. Problem 10: How much heavier is a grain of rice than a strand of hair?

A strand of hair has mass \( 2.17 \times 10^{-5} \) ounces, and a grain of rice is \( 0.002 \) ounces, or \( 2 \times 10^{-3} \) ounces.

The difference is: \[ 2 \times 10^{-3} - 2.17 \times 10^{-5} \]

Converting \( 2 \times 10^{-3} \) into \( 10^{-5} \): \[ 2 \times 10^{-3} = 200 \times 10^{-5} \]

Thus: \[ 200 \times 10^{-5} - 2.17 \times 10^{-5} = (200 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]

In scientific notation: \[ 1.9783 \times 10^{-3} \]

If you need further assistance or clarifications, feel free to ask!

write the answers as a list
1. = 5
2. = 690
etc

Sure! Here are the answers formatted as a list:

  1. = 2
  2. = \( 1.15741 \times 10^{-5} \)
  3. = 27,000,000
  4. = \( 8.9987 \times 10^7 \)
  5. = \( 2.3 \times 10^{-8}, 3.2 \times 10^{-10}, 2.3 \times 10^{-10}, 2.3 \times 10^{-12} \) (in descending order: \( 2.3 \times 10^{-8}, 3.2 \times 10^{-10}, 2.3 \times 10^{-10}, 2.3 \times 10^{-12} \))
  6. = \( 3 \times 10^2 \) kilometers
  7. = \( 2.62 \times 10^6 \) acres
  8. = \( 9.3 \times 10^7 \) miles
  9. = \( 4.7906 \times 10^{-3} \)
  10. = \( 1.9783 \times 10^{-3} \) ounces

If you need any further information or assistance, feel free to ask!

For 5. i will need to write the answers like this __;__;__;__
what do i write?? it seemed too messy to understand to figure out what you were saying

11. Light travels at an approximate rate of 1.9×105%0D%0A1.9%0D%0A×%0D%0A10%0D%0A5%0D%0A mi./sec. There are about 3.2×107%0D%0A3.2%0D%0A×%0D%0A10%0D%0A7%0D%0A seconds in a year. About how many miles does light travel in a year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1 point)%0D%0A miles

12. The average tectonic plate moves at the rate of 0.006 m per year. How many meters would it move in 2×106%0D%0A2%0D%0A×%0D%0A10%0D%0A6%0D%0A years? Write the answer in scientific notation, expressed to the exact decimal place.(1 point)%0D%0A m

13. An asteroid is heading toward Mars at the rate of 7.7×104%0D%0A7.7%0D%0A×%0D%0A10%0D%0A4%0D%0A mi./hr. If the asteroid is 3.311×108%0D%0A3.311%0D%0A×%0D%0A10%0D%0A8%0D%0A 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.(1 point)%0D%0A hours

14. A field of 3.9 mi2%0D%0A3.9%0D%0A %0D%0Ami%0D%0A2%0D%0A is being subdivided into 1.3×103%0D%0A1.3%0D%0A×%0D%0A10%0D%0A3%0D%0A family gardens. How many square miles will there be in each garden? Write the answer in scientific notation.(1 point)%0D%0A mi2

Got it! Here’s how you can structure the answer for question 5 clearly:

  1. = \( 2.3 \times 10^{-12} \); \( 3.2 \times 10^{-10} \); \( 2.3 \times 10^{-10} \); \( 2.3 \times 10^{-8} \)

Now, let's proceed to solve problems 11 to 14.

11. How many miles does light travel in a year?

To find the number of miles light travels in a year:

  • Light speed: \( 1.9 \times 10^{5} \) mi/sec
  • Seconds in a year: \( 3.2 \times 10^{7} \) sec

Light travels:
\[ 1.9 \times 10^{5} , \text{mi/sec} \times 3.2 \times 10^{7} , \text{sec} = 6.08 \times 10^{12} , \text{miles} \]

So the answer is:
11. = \( 6.08 \times 10^{12} \) miles

12. How many meters would the tectonic plate move in \( 2 \times 10^{6} \) years?

To find the distance moved:

  • Rate of movement: \( 0.006 , \text{m/year} \)
  • Years: \( 2 \times 10^{6} \)

Distance moved:
\[ 0.006 , \text{m/year} \times 2 \times 10^{6} , \text{years} = 1.2 \times 10^{4} , \text{meters} \]

So the answer is:
12. = \( 1.2 \times 10^{4} , \text{m} \)

13. How many hours until the asteroid hits Mars?

To find the number of hours until it hits Mars:

  • Speed of the asteroid: \( 7.7 \times 10^{4} \) mi/hr
  • Distance from Mars: \( 3.311 \times 10^{8} \) miles

Time until impact:
\[ \frac{3.311 \times 10^{8} , \text{miles}}{7.7 \times 10^{4} , \text{mi/hr}} = 4.295 \times 10^{3} , \text{hours} \]

So the answer is:
13. = \( 4.295 \times 10^{3} \) hours

14. How many square miles will there be in each garden?

To find the area of each garden:

  • Total area: \( 3.9 , \text{mi}^2 \)
  • Number of gardens: \( 1.3 \times 10^{3} \)

Area per garden:
\[ \frac{3.9 , \text{mi}^2}{1.3 \times 10^{3}} = 3.0 \times 10^{-3} , \text{mi}^{2} \]

So the answer is:
14. = \( 3.0 \times 10^{-3} \) \( \text{mi}^2 \)

Summary of Answers:

  1. = \( 6.08 \times 10^{12} \) miles
  2. = \( 1.2 \times 10^{4} \) m
  3. = \( 4.295 \times 10^{3} \) hours
  4. = \( 3.0 \times 10^{-3} \) \( \text{mi}^2 \)

If you have any more questions or need further clarification, feel free to ask!

9. is 4.79 x 10^-3
13. is 4.3 x 10^3

Thank you for your input! Let's correct those answers based on your observations:

9.Calculate \( 4.8 \times 10^{-3} - 9.4 \times 10^{-6} \)

To perform the calculation:

  1. Convert \( 4.8 \times 10^{-3} \) to the same power of ten as \( 9.4 \times 10^{-6} \):

    • \( 4.8 \times 10^{-3} = 4800 \times 10^{-6} \)

  2. Now subtract: \[ 4800 \times 10^{-6} - 9.4 \times 10^{-6} = (4800 - 9.4) \times 10^{-6} = 4790.6 \times 10^{-6} \]

  3. Converting back to scientific notation: \[ 4790.6 \times 10^{-6} = 4.7906 \times 10^{-3} \]

So, the answer remains as you indicated: 9. = \( 4.79 \times 10^{-3} \)

13. How many hours until it hits Mars?

To find the time:

  1. Divide the distance by the speed: \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{3.311 \times 10^{8} \text{ miles}}{7.7 \times 10^{4} \text{ mi/hr}} \]

  2. Perform the calculation: \[ \text{Time} \approx \frac{3.311}{7.7} \times 10^{8 - 4} \approx 0.430 \times 10^{4} = 4.3 \times 10^{3} \text{ hours} \]

So the corrected answer is: 13. = \( 4.3 \times 10^{3} \) hours

Updated Answers Summary:

  1. = \( 4.79 \times 10^{-3} \)
  2. = \( 4.3 \times 10^{3} \) hours

Thank you for the clarifications! If you have any more questions or corrections, feel free to mention them!

Similar Questions
    1. answers icon 1 answer
    1. answers icon 1 answer
    1. answers icon 1 answer
    1. answers icon 1 answer
more similar questions