Real numbers

The real numbers are every number on the number line: integers, fractions, terminating and recurring decimals, and irrational numbers like $\sqrt{2}$ and $\pi$ whose decimals go on forever without repeating. In this topic you'll sort numbers into these families, learn what a surd is, turn recurring decimals into fractions, sharpen your work with negative numbers, and build exact irrational lengths with a ruler and a set square.

What you'll learn

• 1.01 Rational and irrational numbers: integers, rational numbers, surds and other irrational numbers; recurring decimals as fractions; estimating and ordering roots with and without a calculator.
• 1.02 Operations with integers: the order of operations with negative numbers, powers, nested brackets, fraction bars and negative fractions and decimals, including real-life problems.
• Investigation: construct irrational numbers. Mark $\sqrt{2}$ and $\sqrt{5}$ exactly on a number line, then draw the spiral of Theodorus with a ruler and a set square.

Which level should I pick?

Every worksheet comes in three levels. Each one covers the same skills.

• Level 1 · Warm-up: smaller numbers and more help along the way. A good place to start.
• Level 2 · Core: the main worksheet for the lesson.
• Level 3 · Challenge: harder numbers and multi-step problems, for when the Core level feels easy.

Not sure? Start with Level 2. If the first few questions feel tricky, drop to Level 1. If you finish quickly and get them right, try Level 3. Download the worksheet, print it, and write your answers in the boxes.

Practice tests

When you've finished the lessons, try the three practice tests. Each one is like the real topic test: 45 minutes, 40 marks, a section without a calculator and a section with one. Write your working under each question, then copy your final answers onto the answer sheet on the last page, just like you will in the real test.