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Good Approximations

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.

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Not Continued Fractions

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?

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Comparing Continued Fractions

Which of these continued fractions is bigger and why?

There's a Limit

Stage: 4 and 5 Challenge Level: Challenge Level:1

Explore the continued fraction:

Continued fraction.

What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?