Portfolios Unit 1 Lesson 7
Operations with Scientific Notation Portfolio
You have reached the end of the lesson 01.07 and are ready to show what you know in a project!
You have options to work individually or collaboratively on the project. Since this is the first project, I would recommend you complete Project Option 1 – individual work. However, in case of collaborative project, you and your partner will both need to complete and submit all parts of this project
Instructions
Scientific notation is a tool that is used frequently in science, including astronomy, chemistry, biology, and more. In this activity, imagine that you are a student intern at NASA and are researching information about travel within our solar system. You will complete a series of tasks using what you know about scientific notation and what you discover about our solar system to calculate distances that astronauts may use for their next trip to space.
Part 1
Part 1 is asking you to research the average distance that each planet is from the sun (in kilometers).
To make it consistent for collaboration, I am providing you with distances in the table below. For example, Mercury is located an average of 57,909,000 km from the sun, so on the chart, Mercury would be labeled with a distance of 57,909,000.
Planet
Distance to the Sun in km in standard form
Distance to the Sun in km in scientific notation
Mercury
57,909,000
5.7909x10^7
Venus
108,200,000
Earth
149,600,000
Mars
227,900,000
Jupiter
778,600,000
Saturn
1,443,500,000
Uranus
2,872,500,000
Neptune
4,495,100,000
Part 2
Convert each of the distances that you have recorded into scientific notation. List these on your chart for this assignment. See Mercury example
Part 3
Answer the following questions using the data you have found. Show your work on all questions as indicated.
If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work and provide your answer in scientific notation.
Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer.
If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work.
The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work. Convert your answer into scientific notation if necessary.
.
Part 2:
Planet Distance to the Sun in km in scientific notation
Mercury 5.7909x10^7
Venus 1.082x10^8
Earth 1.496x10^8
Mars 2.279x10^8
Jupiter 7.786x10^8
Saturn 1.4435x10^9
Uranus 2.8725x10^9
Neptune 4.4951x10^9
Part 3:
1. To calculate the distance from Venus to Jupiter, we need to subtract the distance from Venus to the Sun from the distance from Jupiter to the Sun.
Distance from Venus to Jupiter = Distance from Jupiter to the Sun - Distance from Venus to the Sun
= 7.786x10^8 km - 1.082x10^8 km
This equals 6.704x10^8 km in scientific notation.
2. To determine whether the combined distance of Mercury, Venus, and Earth from the Sun is greater or less than the distance from the Sun to Neptune, we need to add up the individual distances for Mercury, Venus, and Earth and compare it to the distance of Neptune from the Sun.
Combined distance of Mercury, Venus, and Earth from the Sun = 5.7909x10^7 km + 1.082x10^8 km + 1.496x10^8 km
This equals 3.1579x10^8 km in scientific notation.
The distance from the Sun to Neptune is 4.4951x10^9 km. Therefore, the combined distance of Mercury, Venus, and Earth from the Sun is less than the distance from the Sun to Neptune.
3. If Earth was 10 times farther away from the Sun than it is now, it would be closest to Uranus. To calculate the distance between Earth and Uranus, we need to find the difference between Earth's new distance and Uranus' distance.
Earth's new distance from the Sun = 1.496x10^8 km x 10
This equals 1.496x10^9 km in scientific notation.
Distance between Earth and Uranus = Earth's new distance from the Sun - Distance from Uranus to the Sun
= 1.496x10^9 km - 2.8725x10^9 km
This equals -1.3765x10^9 km in scientific notation. The negative sign indicates that the distance is in the opposite direction from the Sun.
4. To estimate how many hours it would take the space shuttle to reach Saturn from Earth, we need to divide the distance between Earth and Saturn by the speed of the space shuttle.
Distance between Earth and Saturn = 1.4435x10^9 km
Speed of the space shuttle = 28,000 km/h
Number of hours = Distance between Earth and Saturn / Speed of the space shuttle
= 1.4435x10^9 km / 28,000 km/h
This equals 5.1554x10^4 hours in scientific notation.
weres part 1.
Part 1 is asking you to research the average distance that each planet is from the sun (in kilometers).
To make it consistent for collaboration, I am providing you with distances in the table below. For example, Mercury is located an average of 57,909,000 km from the sun, so on the chart, Mercury would be labeled with a distance of 57,909,000.
Planet
Distance to the Sun in km in standard form
Distance to the Sun in km in scientific notation
Mercury
57,909,000
5.7909x10^7
Venus
108,200,000
Earth
149,600,000
Mars
227,900,000
Jupiter
778,600,000
Saturn
1,443,500,000
Uranus
2,872,500,000
Neptune
4,495,100,000
I apologize for the confusion. Here is Part 1 with the average distance of each planet from the sun in both standard form and scientific notation:
Planet | Distance to the Sun in km (standard form) | Distance to the Sun in km (scientific notation)
------------------------------------------------------------------------------------------------------------------------------
Mercury | 57,909,000 | 5.7909x10^7
Venus | 108,200,000 | 1.082x10^8
Earth | 149,600,000 | 1.496x10^8
Mars | 227,900,000 | 2.279x10^8
Jupiter | 778,600,000 | 7.786x10^8
Saturn | 1,443,500,000 | 1.4435x10^9
Uranus | 2,872,500,000 | 2.8725x10^9
Neptune | 4,495,100,000 | 4.4951x10^9
I hope this clarifies Part 1 for you.
Part 1:
Planet | Distance to the Sun in km (standard form) | Distance to the Sun in km (scientific notation)
Mercury | 57,909,000 | 5.7909x10^7
Venus | 108,200,000 | 1.082x10^8
Earth | 149,600,000 | 1.496x10^8
Mars | 227,900,000 | 2.279x10^8
Jupiter | 778,600,000 | 7.786x10^8
Saturn | 1,443,500,000 | 1.4435x10^9
Uranus | 2,872,500,000 | 2.8725x10^9
Neptune | 4,495,100,000 | 4.4951x10^9
Part 2:
Converted distances in scientific notation added to the chart.
Part 3:
a) Distance between Venus and Jupiter:
To find the distance between the two planets, we subtract the distance from the sun to Venus from the distance from the sun to Jupiter:
Distance = Distance to Jupiter - Distance to Venus
Distance = 7.786x10^8 - 1.082x10^8
Distance = 6.704x10^8 km (Scientific Notation)
b) Combined distance of Mercury, Venus, and Earth from the sun compared to Neptune's distance from the sun:
To find the combined distance of the three planets, we add their individual distances from the sun:
Combined Distance = Distance to Mercury + Distance to Venus + Distance to Earth
Combined Distance = 5.7909x10^7 + 1.082x10^8 + 1.496x10^8
Combined Distance = 3.16x10^8 km (Scientific Notation)
The distance from the sun to Neptune is 4.4951x10^9 km (Scientific Notation).
Since 3.16x10^8 km (Scientific Notation) is less than 4.4951x10^9 km (Scientific Notation), the combined distance of Mercury, Venus, and Earth from the sun is less than the distance from the sun to Neptune.
c) If Earth was 10 times farther away from the sun than it is now, it would be closest to Uranus. To find the new distance between Earth and Uranus, we multiply Earth's current distance by 10:
New Distance to Uranus = Distance to Uranus * 10
New Distance to Uranus = 2.8725x10^9 * 10
New Distance to Uranus = 2.8725x10^10 km (Scientific Notation)
d) To estimate the time it will take the space shuttle to reach Saturn from Earth, we need to divide the distance between the two planets by the speed of the shuttle:
Time = Distance / Speed
Time = 1.4435x10^9 km / 28,000 km/hr
Time = 5.155x10^4 hours (Scientific Notation)
Therefore, it would take approximately 5.155x10^4 hours (Scientific Notation) for the shuttle to reach Saturn from Earth.
To complete Part 2 of the project, you need to convert the distances of each planet into scientific notation. Scientific notation is a way to express numbers that are very large or very small in a more compact form. It is written in the form of "a x 10^n" where "a" is a number between 1 and 10 (inclusive) and "n" is an exponent.
To convert a number into scientific notation, follow these steps:
1. Count the number of decimal places needed to move the decimal point to the right of the first non-zero digit. This will be the value of the exponent "n".
2. Move the decimal point to the right of the first non-zero digit and append "x 10^n". If the decimal point is moved to the left, the exponent will be negative.
Let's use the example of Mercury, which has a distance of 57,909,000 km:
1. Count the number of decimal places needed to move the decimal point to the right of the first non-zero digit. In this case, we need to move the decimal point 7 places to the left.
2. Move the decimal point to the right of the first non-zero digit and insert "x 10^7". The resulting scientific notation for Mercury's distance is 5.7909 x 10^7 km.
Follow the same process for each planet and write down their distances in scientific notation in the chart provided.
For Part 3 of the project, let's address each question one by one:
1. If a spacecraft was parked on Venus and needed to make a flight to Jupiter, you need to calculate the distance it would need to travel. To find this, subtract the distance of Venus from the distance of Jupiter. The answer should be provided in scientific notation.
2. To compare the combined distance of Mercury, Venus, and Earth from the sun with the distance from the sun to Neptune, you need to add up the distances of the three planets and compare it with Neptune's distance. Then, justify your answer.
3. If Earth was 10 times farther away from the sun than it is now, you need to find out which planet it would be closest to. To do this, multiply Earth's current distance by 10 and compare it with the distances of the other planets. Calculate the distance between Earth and the closest planet in both standard notation and scientific notation.
4. To estimate how many hours it will take the shuttle to reach Saturn from Earth, you need to divide the distance between Earth and Saturn by the speed of the space shuttle. Convert your answer into scientific notation if necessary.
Remember to show your work and calculations for each question. Good luck with your project!