Real numbers and standard form
What real numbers and standard form means
You learn to tell which numbers are rational, which are irrational, and which belong to the real number set. You also practise writing very large or very small numbers in standard form, which helps you work neatly and compare values more easily.
What you will practise
- Classify numbers as rational, irrational, or real
- Identify square roots that do not give whole-number answers
- Write large numbers in standard form
- Write small decimal numbers in standard form
- Move the decimal point and count powers of 10
Before you start
You should already be comfortable with whole numbers, fractions, decimals, and square numbers. It also helps if you can place positive and negative numbers on a number line.
Not confident yet? Work through Integers and exponents first.
Worked example
One question from this skill's own question bank, shown with its full working.
Which of these is an irrational number?
- 0.5
- √2
- 3/4
- −7
Working: √2 cannot be written as a fraction of two integers, so it is irrational.
Common mistakes to avoid
- Treating every square root as rational, when some do not simplify to fractions
- Writing standard form with a first number outside 1 to less than 10
- Forgetting that small numbers need negative powers of 10
- Moving the decimal point the wrong way when changing into standard form
Curriculum and exam alignment
This topic normally appears in Junior High School number work, where learners build number sense before later algebra and proportion topics. It is useful preparation for BECE questions that ask you to classify numbers or write values in standard form.
Curriculum notes are a general guide to where this work normally sits. Always check the syllabus your school or examination body is currently using.
Related skills
Other JHS Number & Proportion skills in Maths, at the same point in the course.
Other Maths topics
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Exams that assess real numbers and standard form
Junior High work on this skill feeds directly into these exam papers. Each page lists the Maths topics that appear on it.
How this page was produced
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Practise real numbers and standard form
6 questions with a worked answer after every attempt, and a SmartScore that tracks how close you are to mastery.