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Worksheet Grade 8 Math

Harrowgate PFAS Results: Scientific Notation in Parts Per Trillion

A grade 8 worksheet using a fictional water district's PFAS well results to write very small and very large quantities in scientific notation and compare them.

Objectives

  1. Students will write very large and very small water-testing quantities in scientific notation.
  2. Students will use scientific notation to state how many times as much one measurement is than another.

Vocabulary

Parts per trillion
A unit for measuring extremely small amounts of a chemical in water. PFAS limits are set in parts per trillion because these chemicals matter even in tiny doses.

Also: scientific notation, power of ten

Teacher overview

PFAS are a group of human-made chemicals that water systems measure in extremely small amounts, reported in parts per trillion. Because those numbers are so small, and the volumes of water tested are so large, scientific notation is the natural way to write and compare them. This worksheet uses a fictional water district's test results so students practice both very small and very large powers of ten in one setting. A common mistake to watch for is treating a negative exponent as a negative number; 6 x 10^-1 is 0.6, not a value below zero. EPA set the 4.0 ppt limits for PFOA and PFOS in April 2024, and water systems must meet them by April 2029. In May 2026 EPA proposed letting eligible systems apply for a two-year exemption to April 2031; the proposal was not yet final as of September 2026 and would not change the 4.0 ppt limits. EPA set the limit at about the lowest level that labs can reliably measure, so a real lab would report the 0.6 ppt and 0.03 ppt wells as below its reporting level; those two values are included only for practice with negative exponents.

Harrowgate PFAS Results: Scientific Notation in Parts Per Trillion — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

Harrowgate Water District is a fictional water system that tested three wells for PFAS. One part per trillion (ppt) means one unit of the chemical mixed into one trillion units of water. The federal limit for PFOA and PFOS is 4.0 ppt each. Harrowgate found these PFOA results: Well 1 measured 24 ppt, Well 2 measured 0.6 ppt, and Well 3 measured 120 ppt. Use these results for the problems below. Write each answer in scientific notation as a single digit (or a decimal such as 1.2) times a power of ten.

  1. Write the number one trillion, 1,000,000,000,000, in scientific notation.
  2. Write Well 3's result, 120 ppt, in scientific notation.
  3. Write Well 2's result, 0.6 ppt, in scientific notation.
  4. The limit is 4.0 ppt. How many times as much PFOA is in Well 3 (120 ppt) as the limit allows? Give a whole number, then write it in scientific notation.
  5. How many times as much PFOA is in Well 1 (24 ppt) as the limit of 4.0 ppt?
  6. How many times as much PFOA is in Well 3 (120 ppt) as in Well 2 (0.6 ppt)? Write your answer in scientific notation.
  7. Harrowgate tested 8,000,000 gallons of water during the study. Write 8,000,000 in scientific notation.
  8. A cleaner backup well measured 0.03 ppt. Write 0.03 in scientific notation.
  9. Order these three results from least to greatest: 24 ppt, 0.6 ppt, and 120 ppt.
  10. Well 2 measured 0.6 ppt and the limit is 4.0 ppt. Is Well 2 above or below the limit? Explain how you know.

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 x 10^12.
    One trillion has 12 zeros, so it is 1 followed by 12 places, written 1 x 10^12.
  2. Answer: 1.2 x 10^2.
    120 = 1.2 x 100 = 1.2 x 10^2. Moving the decimal two places left gives the exponent 2.
  3. Answer: 6 x 10^-1.
    0.6 = 6 x 0.1 = 6 x 10^-1. The decimal moves one place right, so the exponent is -1.
  4. Answer: 30 times.
    120 divided by 4 = 30, so Well 3 has 30 times the limit. In scientific notation that is 3 x 10^1.
  5. Answer: 6 times.
    24 divided by 4 = 6, so Well 1 has 6 times the limit. In scientific notation that is 6 x 10^0.
  6. Answer: 2 x 10^2.
    120 divided by 0.6 = 200, and 200 = 2 x 10^2. Well 3 has 200 times the PFOA of Well 2.
  7. Answer: 8 x 10^6.
    8,000,000 is 8 followed by 6 zeros, so it is 8 x 10^6.
  8. Answer: 3 x 10^-2.
    0.03 = 3 x 0.01 = 3 x 10^-2. The decimal moves two places right, so the exponent is -2.
  9. Answer: 0.6, 24, 120.
    Least to greatest is 0.6 ppt, then 24 ppt, then 120 ppt. A smaller number of parts per trillion means less PFAS.
  10. Answer: below the limit.
    0.6 is less than 4.0, so Well 2 is below the 4.0 ppt limit. Comparing the two decimals shows 0.6 < 4.0.

Differentiation

Support

Give students a filled-in reference strip showing the pattern 10^2 = 100, 10^1 = 10, 10^0 = 1, 10^-1 = 0.1, and 10^-2 = 0.01, so they can match each result to the correct power of ten before writing it. Allow them to answer items 4 through 6 with the whole-number quotient first and add the scientific-notation form second.

Extension

Ask students to write each of the three fictional well results as a fraction of the whole (for example, Well 3's 120 ppt as 120 x 10^-12) and then rewrite that product in proper scientific notation with a single digit in front. Have them explain why a larger negative exponent describes a smaller amount of chemical.

ELL supports

Pre-teach "trillion," "power of ten," and "as much as" with a place-value chart that lines up the zeros. Provide a sentence frame for item 10: "Well 2 is ___ the limit because 0.6 is ___ than 4.0."