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Good Approximations

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

Not Continued Fractions

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

Comparing Continued Fractions

Which of these continued fractions is bigger and why?

There's a Limit

Age 14 to 18
Challenge Level

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?


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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