Real numbers and standard form

Junior High 6 questions

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.

Question

Which of these is an irrational number?

0.5
√2
3/4
−7

Answer: √2

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

Ghana GES Basic 7 to 9 syllabusBECE

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.