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Worksheet Grade 8 Math

Ashford County Water by the Numbers: Scientific Notation

A grade 8 worksheet that has students write a fictional water district's large quantities in scientific notation and compare national water figures by magnitude.

Objectives

  1. Students will write large whole numbers in scientific notation.
  2. Students will use scientific notation to compare the size of two quantities.

Vocabulary

Key words: scientific notation, power of ten, magnitude

Teacher overview

Water systems deal in numbers that are hard to picture: hundreds of thousands of customers, billions of gallons, and national repair bills in the hundreds of billions of dollars. Scientific notation turns those long strings of zeros into short, comparable forms. This worksheet uses a fictional utility, the Ashford County Water District, alongside two real national figures so students can practice writing and comparing very large numbers. A common error to watch for is a mismatched exponent: students often count digits instead of counting the places the decimal point moves, so 320,000 gets written as 3.2 × 10^6 rather than 3.2 × 10^5.

Ashford County Water by the Numbers: Scientific Notation — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

Ashford County Water District is a fictional utility. It reported the figures below. For items 1 through 4, write each number in scientific notation.

  • People served: 320,000
  • Water delivered each day: 38,000,000 gallons
  • Main reservoir capacity: 4,500,000,000 gallons
  • Pipe in the ground: 1,200 miles
  1. 320,000 people served.
  2. 38,000,000 gallons delivered each day.
  3. 4,500,000,000 gallons held in the reservoir.
  4. 1,200 miles of pipe.
  5. The reservoir holds 4,500,000,000 gallons. The district delivers 38,000,000 gallons a day. About how many times as much water sits in the reservoir as it sends out in one day? Round to a whole number.
  6. Your answer to item 5 is also about how many days the reservoir would last with no refill. Is that closer to 4 months or to 4 years? Explain in one sentence.
  7. Across the country, EPA estimates that about 4,000,000 lead pipes still need to be replaced. Write 4,000,000 in scientific notation.
  8. A national plan estimates $625,000,000,000 is needed for drinking-water systems over 20 years. Write that dollar amount in scientific notation.
  9. Use item 8. Divide by 20 to find the amount needed each year. Write it in scientific notation, with the front number rounded to the nearest tenth.
  10. The country has about 4,000,000 lead pipes. Ashford serves 320,000 people. About how many times as many lead pipes are there as Ashford has people? Round to the nearest tenth.

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: 3.2 × 10^5 people. Move the decimal point 5 places: 320,000 = 3.2 × 100,000 = 3.2 × 10^5.
  2. Answer: 3.8 × 10^7 gallons. 38,000,000 = 3.8 × 10,000,000 = 3.8 × 10^7.
  3. Answer: 4.5 × 10^9 gallons. 4,500,000,000 = 4.5 × 1,000,000,000 = 4.5 × 10^9.
  4. Answer: 1.2 × 10^3 miles. 1,200 = 1.2 × 1,000 = 1.2 × 10^3.
  5. Answer: about 118 times. Divide: (4.5 × 10^9) ÷ (3.8 × 10^7) = (4.5 ÷ 3.8) × 10^(9-7) = 1.184 × 10^2, which is about 118.
  6. Answer: about 4 months. 118 days is close to 120 days, which is about 4 months; a year is 365 days, so 4 years would be far too long.
  7. Answer: 4 × 10^6 pipes. 4,000,000 = 4 × 1,000,000 = 4 × 10^6.
  8. Answer: 6.25 × 10^11 dollars. 625,000,000,000 = 6.25 × 100,000,000,000 = 6.25 × 10^11.
  9. Answer: about 3.1 × 10^10 dollars. Divide the front number by 20: 6.25 ÷ 20 = 0.3125, so 0.3125 × 10^11. Rewrite with one digit left of the point: 3.125 × 10^10, which rounds to 3.1 × 10^10.
  10. Answer: about 12.5 times. (4 × 10^6) ÷ (3.2 × 10^5) = (4 ÷ 3.2) × 10^(6-5) = 1.25 × 10^1, which is 12.5.

Differentiation

Support

Give students a place-value chart showing where each power of ten sits, and let them count the zeros first, then confirm by counting how many places the decimal point moves. Provide the two national figures already written as a single digit times a power of ten for items 7 and 8, so those items focus only on the comparison.

Extension

Ask students to rank all six quantities on the page from smallest to largest by their power of ten alone, then explain why comparing exponents is faster than comparing the full written numbers. Have them write one new comparison question of their own and answer it.

ELL supports

Pre-teach "power of ten," "digit," and "decimal point" with a labeled example (500 = 5 × 10^2). Provide a sentence frame for the explanation items: "The reservoir holds about ___ times as much because ___." Allow answers to items 6 and 10 to be shown with numbers and a short phrase rather than a full sentence.