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Worksheet Grade 8 Math

Windermoor Water Jobs and Pipes in Scientific Notation

A grade 8 worksheet that writes water-sector job counts, lead service line totals, and a fictional utility's own figures in scientific notation.

Objectives

  1. Students will write large workforce and infrastructure counts in scientific notation.
  2. Students will estimate how many times as large one quantity is than another using powers of ten.
  3. Students will order numbers written in scientific notation.

Vocabulary

Service line
A service line is the small pipe that connects the water main under the street to the plumbing inside one home or building. It is the last leg of the trip water makes to your tap.

Also: scientific notation, power of ten, operator, median

Teacher overview

The numbers that describe the water workforce and the pipes it maintains sit at very different scales, from a few dozen staff at one utility to millions of service lines across the country. Scientific notation lets students hold those scales side by side and say how many times as large one is than another. The worksheet pairs published national figures with the records of a fictional water authority, and it treats the full range of paths into the field, from a state operator license earned after high school to an engineering degree, as equally real options. Teaching note: students routinely write 131,000 as 131 x 10^3 and call it done, because they move the decimal to a comfortable spot rather than to the spot that leaves one digit in front. Ask for the digit count in front of the decimal before you accept any answer.

Windermoor Water Jobs and Pipes in Scientific Notation — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

Write each answer as a single digit, or a short decimal such as 1.32, times a power of ten. Windermoor Regional Water Authority is a fictional utility used in items 8 through 11.

  1. In 2025 the United States employed about 131,000 water and wastewater treatment plant and system operators. Write 131,000 in scientific notation.
  2. About 10,000 openings for water and wastewater operators are projected each year, on average, from 2025 to 2035. Write 10,000 in scientific notation.
  3. Round the job total from item 1 and the yearly openings from item 2 each to a single digit times a power of ten. Then estimate how many times as many operator jobs there are as yearly openings.
  4. EPA estimated in November 2025 that about 4 million lead service lines remain in United States water systems. Write 4,000,000 in scientific notation.
  5. Using 4 x 10^6 lead service lines and 1 x 10^5 operators, estimate the number of lead service lines for each operator.
  6. EPA estimates that $625 billion in drinking-water infrastructure investment is needed over 20 years. Write 625 billion in scientific notation.
  7. Divide the 20-year total from item 6 by 20 to find the amount needed each year. Write that yearly amount in scientific notation.
  8. Windermoor Regional Water Authority serves 96,000 people. Write 96,000 in scientific notation.
  9. Windermoor employs 24 operators. About how many people does each operator serve? Write your answer in scientific notation.
  10. Windermoor plans to replace 1,200 lead service lines. Write 1,200 in scientific notation.
  11. Windermoor wants the 1,200 lines finished in 10 years. How many lines is that each year?
  12. Operators earned a median of $60,020 per year in May 2025. Write 60,020 in scientific notation.
  13. Order these four numbers from least to greatest: 1 x 10^4, 6.002 x 10^4, 1.31 x 10^5, and 4 x 10^6. Which number comes first in your ordered list?
  14. Of those same four numbers, 1 x 10^4, 6.002 x 10^4, 1.31 x 10^5, and 4 x 10^6, which one comes last when they are ordered from least to greatest?
  15. Explain why scientific notation makes it easier to compare 4 x 10^6 with 1.2 x 10^3 than to compare the two numbers written out in full.

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: 1.31 x 10^5.
    The decimal in 131,000 moves five places to the left, which leaves 1.31 and an exponent of 5.
  2. Answer: 1 x 10^4.
    The decimal in 10,000 moves four places to the left, which leaves 1 and an exponent of 4.
  3. Answer: About 10 times.
    131,000 rounds to 1 x 10^5, and 10,000 is already 1 x 10^4. Dividing gives 10^5 divided by 10^4, which is 10^1, or about 10 times as many jobs as yearly openings.
  4. Answer: 4 x 10^6.
    Four million is 4 followed by six zeros, so the exponent is 6.
  5. Answer: 4 x 10^1.
    4 x 10^6 divided by 1 x 10^5 = 4 x 10^1, which is about 40 lead service lines for each operator.
  6. Answer: 6.25 x 10^11.
    625 billion is 625,000,000,000. The decimal moves eleven places to the left, leaving 6.25 and an exponent of 11.
  7. Answer: 3.125 x 10^10.
    625,000,000,000 divided by 20 = 31,250,000,000. The decimal moves ten places to the left, leaving 3.125 and an exponent of 10.
  8. Answer: 9.6 x 10^4.
    96,000 becomes 9.6 after the decimal moves four places to the left.
  9. Answer: 4 x 10^3.
    96,000 divided by 24 = 4,000, and 4,000 is 4 x 10^3 people for each operator.
  10. Answer: 1.2 x 10^3.
    1,200 becomes 1.2 after the decimal moves three places to the left.
  11. Answer: 120 lines per year.
    1,200 divided by 10 = 120 lines each year, which is 1.2 x 10^2.
  12. Answer: 6.002 x 10^4.
    60,020 becomes 6.002 after the decimal moves four places to the left.
  13. Answer: 1 x 10^4.
    Compare exponents first. Two of the four numbers have exponent 4, which is the smallest exponent in the list, and 1 is less than 6.002, so 1 x 10^4 comes first.
  14. Answer: 4 x 10^6.
    The exponent 6 is larger than any other exponent in the list, so 4 x 10^6 comes last. The full order from least to greatest is 1 x 10^4, 6.002 x 10^4, 1.31 x 10^5, 4 x 10^6.
  15. Answer: The exponents show the size at a glance.
    Written out, the two numbers are 4,000,000 and 1,200, and a reader has to count digits. In scientific notation the exponents 6 and 3 differ by 3, so 4 x 10^6 is more than a thousand times as large as 1.2 x 10^3, which a reader can see before doing any long division.

Differentiation

Support

Give students a place-value strip that runs from 10^0 through 10^12 with the words thousand, million, and billion written under the matching powers. Let them slide a finger along the strip while moving the decimal, and allow items 3 and 5 to be answered with the rounded whole numbers before the scientific notation form is added.

Extension

Ask students to research the size of their own local water system, or to use the fictional Windermoor figures, and to build a table that expresses the population served, the staff count, and the miles of pipe in scientific notation. Have them write one sentence comparing two of those quantities using a power of ten.

ELL supports

Pre-teach median, service line, and power of ten with a labeled diagram of a pipe running from a street main into a house. Provide the sentence frame for items 3 and 5: "There are about ___ times as many ___ as ___."

Extensions

Invite a local utility staff member to describe the paths people took into their jobs, which may include a state operator license earned after high school, a two-year technical certificate, or a four-year engineering degree. Have students write the size of that utility's service population in scientific notation and compare it with the fictional Windermoor figure from item 8.