Resources tagged with: Rational and irrational numbers

Filter by: Content type:
Age range:
Challenge level:

There are 23 NRICH Mathematical resources connected to Rational and irrational numbers, you may find related items under The Number System and Place Value.

Broad Topics > The Number System and Place Value > Rational and irrational numbers

Repetitiously

Age 14 to 16
Challenge Level

Can you express every recurring decimal as a fraction?

An Introduction to Irrational Numbers

Age 14 to 18

Tim Rowland introduces irrational numbers

Irrational Arithmagons

Age 16 to 18
Challenge Level

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

The Clue Is in the Question

Age 16 to 18
Challenge Level

Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

Road Maker 2

Age 16 to 18 Short
Challenge Level

Can you work out where the blue-and-red brick roads end?

Impossible Triangles?

Age 16 to 18
Challenge Level

Which of these triangular jigsaws are impossible to finish?

The Square Hole

Age 14 to 16
Challenge Level

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

Equal Equilateral Triangles

Age 14 to 16
Challenge Level

Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Impossible Square?

Age 16 to 18
Challenge Level

Can you make a square from these triangles?

What Are Numbers?

Age 7 to 18

Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.

Spirostars

Age 16 to 18
Challenge Level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

An Introduction to Proof by Contradiction

Age 14 to 18

An introduction to proof by contradiction, a powerful method of mathematical proof.

The Dangerous Ratio

Age 11 to 14

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying.

All Is Number

Age 7 to 14

Read all about Pythagoras' mathematical discoveries in this article written for students.

Rational Round

Age 16 to 18
Challenge Level

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

Proof Sorter - the Square Root of 2 Is Irrational

Age 16 to 18
Challenge Level

Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.

Approximations, Euclid's Algorithm & Continued Fractions

Age 16 to 18

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

Continued Fractions II

Age 16 to 18

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).

Making Rectangles, Making Squares

Age 11 to 14
Challenge Level

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Rationals Between...

Age 14 to 16
Challenge Level

What fractions can you find between the square roots of 65 and 67?

Rational Roots

Age 16 to 18
Challenge Level

Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.

Good Approximations

Age 16 to 18
Challenge Level

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

Be Reasonable

Age 16 to 18
Challenge Level

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.