Learning Goal
Part of: Know that there are numbers that are not rational, and approximate them by rational numbers — 2 of 2 cluster items
Use rational approximations of irrational numbers
**8.NS.A.2**: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of sqrt(2), show that sqrt(2) is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
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8.NS.A.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi^2). For example, by truncating the decimal expansion of sqrt(2), show that sqrt(2) is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.
What you'll learn
- Approximate an irrational number by successively narrowing the interval between two rational bounds (e.g., showing that sqrt(2) is between 1.41 and 1.42 by squaring both endpoints)
- Locate irrational numbers on a number line diagram to a specified degree of precision using rational approximations
- Compare the size of two irrational numbers by computing rational approximations of each to enough decimal places to determine which is larger
- Estimate the value of expressions involving irrational numbers (e.g., pi^2, 3sqrt(5)) by substituting rational approximations and computing
- Explain why rational approximations of irrational numbers can be made arbitrarily close but never exact, and describe how to obtain a better approximation
Slides
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Slides
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