Water for Schools
Menu

Worksheet Grade 8 Math

Basalt Bluff Reservoirs: Comparing Volumes in Scientific Notation

A grade 8 worksheet where students convert four fictional reservoirs' acre-foot volumes to gallons and compare their sizes using scientific notation.

Objectives

  1. Students will convert a volume in acre-feet to gallons and express the result in scientific notation.
  2. Students will divide numbers written in scientific notation to compare two quantities.
  3. Students will explain how the exponent in scientific notation reflects a quantity's size.

Vocabulary

Acre-foot
The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: scientific notation, significant figures

Teacher overview

Water districts often measure reservoir volume in acre-feet, a unit sized for large-scale water storage rather than a single household. This worksheet has students convert four reservoirs' acre-foot volumes to gallons and write the results in scientific notation, the tool mathematicians and scientists use to work with very large numbers without writing out a string of zeros. A common misconception here is dropping or misplacing a zero during the acre-foot-to-gallon conversion before converting to scientific notation, which throws off the exponent even when the leading digit is correct; encourage students to estimate the size of their answer before finalizing it.

Basalt Bluff Reservoirs: Comparing Volumes in Scientific Notation — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

Basalt Bluff Water District (a fictional water district used for this worksheet) stores water in four reservoirs. Each reservoir's size is measured in acre-feet. One acre-foot equals 325,851 gallons. Use this conversion for every problem below. Round each scientific notation answer to three significant figures unless a problem tells you otherwise.

  1. Convert Northgate Tank's volume of 3 acre-feet to gallons. Write your answer in scientific notation.
  2. Convert Ridge Reservoir's volume of 90 acre-feet to gallons. Write your answer in scientific notation.
  3. Convert Valley Reservoir's volume of 2,700 acre-feet to gallons. Write your answer in scientific notation.
  4. Convert Highland Reservoir's volume of 81,000 acre-feet to gallons. Write your answer in scientific notation.
  5. Look at your answers to problems 1 and 4. How many times as much water does Highland Reservoir hold compared to Northgate Tank? Show the division in scientific notation.
  6. Look at your answers to problems 2 and 3. How many times as much water does Valley Reservoir hold compared to Ridge Reservoir?
  7. Rank all four reservoirs from smallest to largest by gallon volume. Use your answers from problems 1 through 4.
  8. A fifth, new reservoir holds exactly ten times as much water as Highland Reservoir. Without converting acre-feet again, use scientific notation to find its volume in gallons.
  9. A number is already written in scientific notation. Explain, using place value, why multiplying it by 10 changes only the exponent, not the leading digit.
  10. An engineer says Valley Reservoir holds "almost a billion gallons." Use your answer from problem 3. Is this description close to correct? Explain your reasoning.

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: 9.78×10^5 gal.
    3 × 325,851 = 977,553 gallons, which in scientific notation rounded to three significant figures is 9.78 × 10^5.
  2. Answer: 2.93×10^7 gal.
    90 × 325,851 = 29,326,590 gallons, or 2.93 × 10^7 rounded to three significant figures.
  3. Answer: 8.80×10^8 gal.
    2,700 × 325,851 = 879,797,700 gallons, or 8.80 × 10^8 rounded to three significant figures.
  4. Answer: 2.64×10^10 gal.
    81,000 × 325,851 = 26,393,931,000 gallons, or 2.64 × 10^10 rounded to three significant figures.
  5. Answer: 2.7×10^4 times.
    Dividing the exact volumes, 26,393,931,000 ÷ 977,553 = 27,000, which is 2.7 × 10^4. Highland holds 27,000 times as much water as Northgate.
  6. Answer: 30 times.
    879,797,700 ÷ 29,326,590 = 30. Valley holds 30 times as much water as Ridge, matching the fact that 2,700 acre-feet is 30 times 90 acre-feet.
  7. Answer: Northgate, Ridge, Valley, Highland.
    Comparing the exponents and leading digits from problems 1 through 4 (10^5 through 10^10) gives this order from smallest to largest.
  8. Answer: 2.64×10^11 gal.
    Multiplying Highland's volume (2.64 × 10^10) by 10 shifts the exponent up by one, giving 2.64 × 10^11 gallons.
  9. Answer: the exponent increases by one while the leading digit stays the same.
    Multiplying by 10 shifts every digit one place value to the left, which is exactly what increasing the power of 10 by one does; the leading digit does not change because no digit is added or removed, only shifted in place value.
  10. Answer: yes, reasonably accurate.
    Valley Reservoir holds about 8.80 × 10^8 gallons, or 880 million gallons, which is close to but not quite a billion (1 × 10^9) gallons. Describing it as "almost a billion gallons" is a fair, if slightly generous, description.

Differentiation

Support (below grade level)

Provide a printed reference card showing a fully worked example of one acre-foot-to-gallon conversion in scientific notation (using a fifth reservoir not in the worksheet), and allow students to use a calculator for every multiplication and division step.

Extension (above grade level)

Ask students to determine how many acre-feet a reservoir would need to hold exactly 1.0 × 10^9 gallons (one billion gallons), working backward from the acre-foot-to-gallon conversion, and to compare that acre-foot figure with Valley Reservoir's stated 2,700 acre-feet.

ELL supports

Pre-teach "acre-foot," "exponent," and "significant figures" with a simple visual showing a football-field-sized area one foot deep next to a labeled gallon jug. Allow students to show scientific notation answers in a table with separate columns for "leading digit" and "exponent" instead of full sentences for problems 1 through 4.