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Worksheet Grade 8 Science

Lake Sable Reservoir in Scientific Notation: A Dam Worksheet

Grade 8 students at the fictional Sable River Dam write reservoir capacity, downstream releases, and hydropower figures in scientific notation and compare their sizes.

Objectives

  1. Students will write large water and energy quantities in scientific notation.
  2. Students will compare two quantities in scientific notation to estimate how many times larger one is than the other.

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.
Reservoir
A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
Hydropower
Electricity made from moving water, usually water falling through a dam. It is a renewable power source that can start up quickly when the electric grid needs it.

Also: scientific notation

Teacher overview

Reservoirs hold huge amounts of water, and dams produce large amounts of power, so the numbers behind them run into the billions. This worksheet uses the fictional Sable River Dam to give students a real reason to write and compare numbers in scientific notation. Apart from the Hoover Dam comparison, every value is either a stated conversion or a made-up figure for this dam, so students can focus on the notation itself.

Lake Sable Reservoir in Scientific Notation: A Dam Worksheet — Grade 8 Science
Name: ____________________________ Date: ______________

Student Worksheet

The town of Ridgeway (a fictional town) owns the Sable River Dam. The dam holds back a reservoir called Lake Sable. When full, Lake Sable holds 48,000 acre-feet of water. One acre-foot equals 325,851 gallons. Use these facts for the items below, and write large answers in scientific notation with two significant figures unless told otherwise.

  1. Write 48,000 acre-feet in scientific notation.
  2. Convert Lake Sable's full capacity to gallons by multiplying 48,000 by 325,851. Then write your answer in scientific notation with two significant figures.
  3. A farm pond near Ridgeway holds about 2.0 × 10^6 gallons. Using your rounded answer from item 2, about how many times more water does Lake Sable hold than the farm pond?
  4. The dam releases 5.0 × 10^5 gallons downstream each day to protect fish habitat. How many gallons is that over a 30-day month? Write your answer in scientific notation.
  5. Compare the daily release of 5.0 × 10^5 gallons to Lake Sable's full capacity of about 1.6 × 10^10 gallons. About how many days of releases would it take to empty a full Lake Sable if no new water flowed in?
  6. Explain in one or two sentences why scientific notation is easier to work with here than writing out all the digits of Lake Sable's capacity.
  7. Ridgeway's power plant at the dam can produce 24 megawatts. The real Hoover Dam power plant is rated to produce about 2,080 megawatts, although years of drought and low water in Lake Mead have cut the power it actually makes by about 30 percent. Using the rated 2,080 megawatts, about how many times more powerful is Hoover Dam's plant than Ridgeway's?
  8. Write Hoover Dam's capacity of about 2,080 megawatts in scientific notation with two significant figures.
  9. During a spring flood, the reservoir rose by 3.0 × 10^3 acre-feet in one week. If it kept rising at that same weekly rate, how much would it rise in 4 weeks? Write your answer in scientific notation.
  10. Lake Sable started that flood at 48,000 acre-feet and then rose 1.2 × 10^4 acre-feet over 4 weeks. A safety limit is set at 6.5 × 10^4 acre-feet. Add the two amounts and decide whether the reservoir stays below the limit.

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: 4.8 × 10^4 acre-feet.
    Move the decimal point four places: 48,000 becomes 4.8 × 10^4.
  2. Answer: 1.6 × 10^10 gallons.
    48,000 × 325,851 = 15,640,848,000 gallons. Rounded to two significant figures, that is 1.6 × 10^10 gallons.
  3. Answer: About 8,000 times.
    1.6 × 10^10 ÷ (2.0 × 10^6) = 0.8 × 10^4 = 8.0 × 10^3, which is about 8,000 times.
  4. Answer: 1.5 × 10^7 gallons.
    5.0 × 10^5 × 30 = 150 × 10^5 = 1.5 × 10^7 gallons.
  5. Answer: 3.2 × 10^4 days.
    1.6 × 10^10 ÷ (5.0 × 10^5) = 0.32 × 10^5 = 3.2 × 10^4, which is 32,000 days.
  6. Answer: Scientific notation is shorter and easier to compare.
    Writing 1.6 × 10^10 shows the size at a glance, while 15,640,848,000 is long and easy to miscount. Accept any clear explanation that mentions length or ease of comparison.
  7. Answer: About 87 times.
    2,080 ÷ 24 = 86.67, which rounds to about 87 times.
  8. Answer: 2.1 × 10^3 megawatts.
    2,080 rounds to 2.1 × 10^3 (two significant figures).
  9. Answer: 1.2 × 10^4 acre-feet.
    3.0 × 10^3 × 4 = 12 × 10^3 = 1.2 × 10^4 acre-feet.
  10. Answer: 6.0 × 10^4 acre-feet, which stays below the limit.
    48,000 + 12,000 = 60,000 = 6.0 × 10^4 acre-feet. Since 6.0 × 10^4 is less than 6.5 × 10^4, the reservoir stays under the safety limit.

Differentiation

Support

Give students a printed reference strip showing how to move the decimal point for powers of ten, plus one fully worked example (a different reservoir, such as 90,000 acre-feet) before item 1. Allow calculator use for the multiplication in item 2 and confirm the long product before students convert it to scientific notation.

Extension

Ask students to calculate, using only the numbers on this worksheet, how many farm ponds (each 2.0 × 10^6 gallons) it would take to equal Lake Sable, and to express the answer both as a whole number and in scientific notation. Then have them design a third reservoir with a capacity between the farm pond and Lake Sable and write it in scientific notation.

ELL supports

Pre-teach "reservoir," "release," and "capacity" with a labeled sketch of a dam holding back a lake, with an arrow for the downstream release. Provide a sentence frame for item 6 and the other explanation parts: "Scientific notation is easier because ___." Allow answers to be shown as calculations plus a short phrase rather than full sentences.