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Math problem set Grade 8 Careers & CTE

Reporting a Plant's Numbers: Scientific Notation on the Job

A grade 8 math set where students write a fictional treatment plant's daily and yearly water figures in scientific notation and compare capacities across plants.

Objectives

  1. Students will write large water-plant quantities in proper scientific notation.
  2. Students will compare two plant capacities by finding how many times larger one is than the other.

Vocabulary

Flow rate
Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: scientific notation, power of 10, coefficient

Teacher overview

Operators and engineers report plant numbers so large that scientific notation is the clearest way to write them. This set follows a fictional treatment plant as a new operator prepares a capacity report. Students write daily and yearly flows in scientific notation and compare plants by size. A common mistake this set targets is writing a value like 12,000,000 as 12 × 10 to the sixth; the coefficient must be at least 1 and less than 10, so the correct form is 1.2 × 10 to the seventh.

Reporting a Plant's Numbers: Scientific Notation on the Job — Grade 8 Careers & CTE
Name: ____________________________ Date: ______________

Problems

The fictional Cypress Bend Regional Water Plant treats 12 MGD, which is 12,000,000 gallons of water each day. Use these facts for the problems below:

  • One million gallons per day equals 694 gallons per minute.
  • One person uses about 100 gallons of water per day.
  1. Write the plant's daily flow of 12,000,000 gallons in scientific notation.
  2. Convert the plant's flow of 12 MGD to gallons per minute using 694 gallons per minute per MGD, then write that result in scientific notation.
  3. The plant runs every day of a 365-day year. Find the plant's total yearly flow and write it in scientific notation.
  4. A smaller nearby plant treats 3,000,000 gallons per day. Write that daily flow in scientific notation, then find how many times larger Cypress Bend's daily flow is.
  5. A large metro system treats 1.2 × 10^9 gallons per day. How many times larger is that than Cypress Bend's daily flow?
  6. If each person uses about 100 gallons per day, about how many people can Cypress Bend's 12,000,000 gallons per day serve? Write the answer in scientific notation.
  7. Find the combined daily flow of Cypress Bend (12,000,000 gallons) and the smaller plant (3,000,000 gallons), and write the total in scientific notation.
  8. A new operator writes the daily flow as 12 × 10^6 gallons. Explain why this is not proper scientific notation, and give the correct form.

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: 1.2 × 10^7 gallons. Move the decimal 7 places: 12,000,000 becomes 1.2, and the decimal moved 7 places, so the power is 10^7.
  2. Answer: 8,328 gpm. 12 × 694 = 8,328 gallons per minute. In scientific notation that is about 8.3 × 10^3 gpm (8,328 rounded to 8.3 with the decimal moved 3 places).
  3. Answer: 4.38 × 10^9 gallons. 12,000,000 × 365 = 4,380,000,000, and moving the decimal 9 places gives 4.38 × 10^9.
  4. Answer: 4 times. 3,000,000 = 3 × 10^6. Cypress Bend is 1.2 × 10^7, so (1.2 × 10^7) ÷ (3 × 10^6) = 0.4 × 10^1 = 4, so Cypress Bend's daily flow is 4 times larger.
  5. Answer: 100 times. (1.2 × 10^9) ÷ (1.2 × 10^7) = 10^(9−7) = 10^2 = 100 times larger.
  6. Answer: 1.2 × 10^5 people. 12,000,000 ÷ 100 = 120,000 people, and moving the decimal 5 places gives 1.2 × 10^5.
  7. Answer: 1.5 × 10^7 gallons. 12,000,000 + 3,000,000 = 15,000,000, and moving the decimal 7 places gives 1.5 × 10^7.
  8. Answer: The coefficient must be at least 1 and less than 10, and 12 is too large. The value 12,000,000 is correct, but proper scientific notation writes it as 1.2 × 10^7, not 12 × 10^6.

Differentiation

Support

Give students a place-value strip showing 12,000,000 with the decimal point and arrows counting the moves, and let them practice on 30,000 and 500,000 before problem 1. Provide the division setup for problem 4 already written as (1.2 × 10^7) ÷ (3 × 10^6).

Extension

Ask students to express the plant's yearly flow (from problem 3) in gallons per second in scientific notation, showing every conversion step from years to seconds.

ELL supports

Pre-teach "scientific notation," "coefficient," and "power of 10" with a labeled example showing the single-digit rule. Allow students to record answers as the coefficient and exponent in separate labeled boxes rather than writing full sentences.