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Interactive

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In this Cyberchase interactive game, Hacker has removed some of the tracks on the Trans-Cyberspace Railroad. The challenge is to repair the tracks so that the Cybertrain can get back to the central station. A set of spare tracks that range in length from 0.1 to 1.0 will be used to fill in the gaps. In many cases it will be necessary to use a combination of two or three pieces to fill in the missing part of the track. All the gaps on the screen must be filled before the train will move.

Background Essay

You can describe many quantities with a whole number—the number of students in a classroom, the number of soda cans sold at lunch, the number of tennis balls you own. But other quantities cannot be described using a whole number—such as the number of inches a person grew last year or the amount of money in your wallet. When you need to describe a part of the whole, you must use fractions and decimals.

Fractions use the idea of sharing or dividing, while decimals extend the place value system to include tenths, hundredths, thousandths, and so on. You can write a quantity in either fractional or decimal notation, but the situation may require one form rather than the other. We commonly use fractions to describe measurements in construction and cooking. We commonly use decimals in financial applications, in scientific measurements and distance, and when using a standard calculator.

Decimals allow you to describe quantities smaller than one, and they allow you to combine these quantities with whole numbers. For example, instead of saying "three plus one-half," we can write 3.5. Decimals also allow for a more precise measurement in many cases since they extend the place value system to the level of accuracy you can measure.

When adding or subtracting decimals it is important to consider the precision, or the number of decimal places each number has. By lining up the decimal points before completing the addition, you can be certain that you are combining the correct values. In some cases, it is appropriate to round numbers to the nearest tenth or hundredth in order for all numbers to have the same level of precision. Your combined value can only be as precise as the least precise measurement in the set of numbers.

To learn more about decimal additions, check out How Many Rails for the Detour?, How Far to Wells Road?, and Several Short Rails Make More Than A Whole.

Discussion Questions

• How did you decide which pieces to use to fill a particular gap?
• How many different combinations of two pieces will yield a length of 1.1 units using the pieces given? If we're not limited to using just two pieces, how many combinations would there be?
• What is the longest length of track that could be missing and still be repaired?
• In your home or school, can you find examples of numbers expressed as decimals? What are they?

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