Launching Into Expressions and Equations

International Space StationInternational Space Station

In this mission, you will join the crew of the International Space Station, a research laboratory that orbits the Earth. It's the largest structure that humans have ever put into space! While aboard, you and your crew members will conduct many scientific experiments in biology, physics, astronomy, and more. You will collect huge amounts of data, including very large and very small numbers. You will need to use your knowledge of scientific notation to help analyze and communicate your findings. Grab a pencil and paper for calculations, and get ready for an out-of-this-world adventure!

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Begin Training
You arrive at the Johnson Space Center in Houston, Texas, ready to train in an International Space Station (ISS) model that sits at the bottom of a pool. The pool helps astronauts experience how it feels to be weightless while moving about and working on the ISS in space. The pool holds 22,700,000 liters of water. Express this quantity in scientific notation.
  1. 7 x 2.2710
  2. 227 + 105
  3. 2.27 x 107
  4. 7 + 2.2710
That’s not correct.
Check your calculations and try again.
That is the correct answer. Well done!
Answer: C
Hint: Remember to move the decimal point until the coefficient is greater than or equal to 1 but less than 10. Multiply that coefficient by a power of 10. The power is the number of times the decimal point moved.
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Zero-Gravity Training

Your mission in space orbiting the earth is planned to last 186 days, or 1.60704 x 107 seconds, from launch to return. During your training, you spend time in the "Weightless Wonder," a plane that gives you experience with 2.5 x 101 seconds of microgravity (often called "zero gravity," in which people and objects seem weightless and float in air).

How many times longer will you have to bear microgravity in space than during your time in the Weightless Wonder?

  1. 6.42816 x 105
  2. 4.0176 x 108
  3. 0.642816 x 106
  4. 4.10704 x 108
That’s not correct.
Check your calculations and try again.
That is the correct answer. Well done!
Answer: A
Hint:

Recall that when you divide powers of 10, you can simply subtract their exponents.

Also, remember to adjust if the coefficient is less than 1 or greater than or equal to 10.

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Gene Research
One of your mission goals is to study how microgravity influences genes. To do this, you and your team will conduct experiments with yeast cells, which measure 0.0000036 meters in diameter. Express this length in scientific notation.
  1. 3.6 x 106
  2. 36 x 10-5
  3. .36 x 107
  4. 3.6 x 10-6
That’s not correct.
Check your calculations and try again.
That is the correct answer. Well done!
Answer: D
Hint: Remember that the power of 10 for numbers less than 1 should be negative.
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Travel Distance
The International Space Station travels 2.88 x 104 kilometers per hour in its orbit around Earth. How many kilometers will you travel during your entire mission of 186 days?
  1. 5.3568 x 106
  2. 12.85632 x 107
  3. 1.285632 x 108
  4. 2.232 x 105
That’s not correct.
Check your calculations and try again.
That is the correct answer. Well done!
Answer: C
Hint: Remember to convert the number of days of your mission (186) into hours.
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Leaving the International Space Station
You are about to return to Earth, whose mass is 5.9723 x 1024 kilograms and which causes a great gravitational pull. It's time to say good-bye to the International Space Station, whose mass is about 7.03 x 10–20 times the size of Earth. This results in a much weaker gravitational pull. What is the approximate mass, in kilograms, of the International Space Station?
  1. 1.1771 x 104
  2. 4.2 x 105
  3. 1.30023 x 105
  4. 8.49545 x 103
That’s not correct.
Check your calculations and try again.
That is the correct answer. Well done!
Answer: B
Hint:

Remember that when you multiply powers of 10, you can simply add their exponents.

Also, remember to adjust if the coefficient is less than 1 or greater than or equal to 10.

Congratulations! You've Succeeded in Your Mission!
Back to Home
Bonus Mission Task: Think It Through
The pool at Johnson Space Center holds 22,700,000 liters, or 22.7 megaliters, of water. Why might someone want to express this amount as 22,700,000 liters? Why might someone want to express this amount as 22.7 megaliters?

Bonus Mission Task: Think It Through

It might be helpful to express the amount as liters so as to better visualize the amount. People have lots of experience with real-life items measured in liters (such as 2-liter bottles of soda), so expressing the amount using this unit might be easier to visualize. On the other hand, it is more efficient to express the amount in megaliters, as the number is shorter (it has less zeros). Additionally, this shorter number might leave less room for error when using it in calculations.
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Bonus Mission Task: Think It Through

Now assume your mission is twice the length it was before. The Weightless Wonder lets you experience twice the amount time in microgravity than before due to advances in the technology. How many times longer will you now have to bear microgravity in space than during your time in the Weightless Wonder?

Bonus Mission Task: Think It Through

The answer remains 6.42816 x 105. Multiply both the mission time and the time the Weightless Wonder allows by 2. Since both numbers are being multiplied by a factor of 2, the answer does not change. (2 x 1.60704 x 107) / (2 x 2.5 x 101) = 6.42816 x 105.

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Bonus Mission Task: Think It Through
A yeast cell measures 0.0000036 meters in diameter. How many kilometers is the diameter? Centimeters? Millimeters?

Bonus Mission Task: Think It Through

0.0000036 meters = 3.6 x 10-6 meters

0.0000000036 kilometers = 3.6 x 10-9 kilometers

0.00036 centimeters = 3.6 x 10-4 centimeters

0.0036 millimeters = 3.6 x 10-3 millimeters

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Bonus Mission Task: Think It Through

Now assume your entire mission lasts 2.6784 x 105 minutes. How many kilometers will you travel if your speed is still 2.88 x 104 kilometers per hour? What do you notice?

Bonus Mission Task: Think It Through

2.88 x 104 / 60 x 2.6784 x 105 = 1.285632 x 108. The distances are the same because the trip time did not change. 186 days = 2.6784 x 105 minutes.

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Bonus Mission Task: Think It Through
When is it helpful to describe quantities with scientific notation?

Bonus Mission Task: Think It Through

It is helpful to describe quantities with scientific notation when the numbers are very small or very large. This is when there are strings of zeros (or other values) at the end of a very large number or right after a decimal. The format of scientific notation might leave less room for error in writing or calculating, especially if there are a lot of zeros. It can also be easier and faster to understand the size of a number through a power-of-ten exponent rather than through counting up many zeros.
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