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Worksheet Grade 8 Math

Saltcote Desalination: Scientific Notation for Plant Volumes

A grade 8 worksheet using a fictional desalination plant's daily flows and membrane pore sizes to write and compare quantities in scientific notation.

Objectives

  1. Students will write large and small quantities in scientific notation.
  2. Students will use scientific notation to state how many times as large one quantity is than another.

Vocabulary

Reverse osmosis
Reverse osmosis cleans water by pushing it through a membrane with holes so tiny that salt and most other dissolved things cannot fit through. It can even turn seawater into fresh water.

Also: scientific notation, membrane, concentrate

Teacher overview

Saltcote is a fictional coastal town that makes drinking water by pushing seawater through reverse osmosis membranes. The numbers in this system run from millions of gallons a day down to pore openings far smaller than a grain of sand, so it is a clear place to practice scientific notation. A common mistake is writing a number like 40,000,000 as 4 x 10^8 by counting all the digits instead of counting the places after the leading digit; every item below rewards checking the exponent against the size of the number.

Saltcote Desalination: Scientific Notation for Plant Volumes — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

Saltcote runs a fictional reverse osmosis plant. Use these stated values for the problems below.

  • The plant makes 4,000,000 gallons of drinking water each day.
  • The plant pulls in 10,000,000 gallons of seawater each day.
  • Each storage tank holds 500,000 gallons.
  • One membrane pore is about 0.0000000005 meter across.
  • A grain of sand is about 0.0005 meter across.
  1. Write the daily drinking water, 4,000,000 gallons, in scientific notation.
  2. Write the daily seawater intake, 10,000,000 gallons, in scientific notation.
  3. Using your answers to items 1 and 2, how many times as much seawater as drinking water does the plant handle each day?
  4. Write the membrane pore size, 0.0000000005 meter, in scientific notation.
  5. Write the grain of sand size, 0.0005 meter, in scientific notation.
  6. Using your answers to items 4 and 5, how many times as wide is a grain of sand as one pore? Write the answer in scientific notation.
  7. The plant makes 4 x 10^6 gallons every day. How much does it make in 365 days? Write the answer in scientific notation.
  8. Each tank holds 5 x 10^5 gallons. How many full tanks would one day of drinking water, 4 x 10^6 gallons, fill?
  9. Water leaves the plant as drinking water, 4 x 10^6 gallons, plus leftover concentrate. If the concentrate is 6 x 10^6 gallons, add the two. Does the total match the daily intake from item 2?
  10. Explain your reasoning: Why is scientific notation more helpful for comparing the pore size and the grain of sand than for comparing 4,000,000 and 4,100,000?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 4 x 10^6 gallons.
    Move the decimal point 6 places to the left, from 4,000,000 to 4. The exponent is 6.
  2. Answer: 1 x 10^7 gallons.
    10,000,000 is a 1 followed by 7 zeros, so it is 1 x 10^7.
  3. Answer: 2.5 times.
    Divide the intake by the drinking water: (1 x 10^7) / (4 x 10^6) = 10,000,000 / 4,000,000 = 2.5.
  4. Answer: 5 x 10^-10 meter.
    0.0000000005 has the 5 in the tenth place after the decimal point, so the exponent is negative 10.
  5. Answer: 5 x 10^-4 meter.
    0.0005 has the 5 in the fourth place after the decimal point, so the exponent is negative 4.
  6. Answer: 1 x 10^6 times.
    Divide: (5 x 10^-4) / (5 x 10^-10). The 5s divide to 1, and 10^-4 divided by 10^-10 is 10^6, so the sand is 1 x 10^6 times as wide.
  7. Answer: 1.46 x 10^9 gallons.
    4 x 10^6 times 365 = 1,460,000,000 gallons, which is 1.46 x 10^9 gallons.
  8. Answer: 8 tanks.
    (4 x 10^6) / (5 x 10^5) = 4,000,000 / 500,000 = 8 tanks.
  9. Answer: 1 x 10^7 gallons.
    4 x 10^6 + 6 x 10^6 = 10 x 10^6 = 1 x 10^7 gallons, which matches the daily intake in item 2.
  10. Answer: The pore and the sand grain differ by many powers of ten, so scientific notation shows the size gap at a glance; 4,000,000 and 4,100,000 are close in size, so ordinary form compares them just as clearly.

Differentiation

Support

Give students a place-value strip that shows the decimal point moving one step per power of ten, and let them practice items 1 and 2 by counting zeros aloud before writing the exponent. Provide the division setups already written for items 3 and 6.

Extension

Ask students to find how many days the plant would run to make 1 x 10^9 gallons of drinking water, working backward from the daily rate in item 7 and writing the number of days in ordinary form and in scientific notation.

ELL supports

Pre-teach "membrane," "pore," "intake," and "concentrate" with a simple labeled sketch of seawater entering, drinking water leaving one side, and salty concentrate leaving the other. Provide a sentence frame for item 10: "Scientific notation helps more when two numbers are ___ in size."