Rational Numbers
Numbers expressible as p/q with integers p, q, q≠0.
Key idea
Numbers expressible as p/q with integers p, q, q≠0.
In depth
A rational number can be written as a fraction p/q of integers with q ≠ 0. Its decimal expansion either ends or repeats. Includes all integers, finite decimals and repeating decimals.
Worked example
0.25 = 1/4, −3 = −3/1, 0.666... = 2/3 are all rational.
Formula
Real-world uses
- Representing exact ratios such as 3/7 in engineering
- Expressing repeating decimals as fractions
Common mistake
Assuming a long non-repeating-looking decimal is irrational. Check the pattern or the definition.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Rational Numbers?
Numbers expressible as p/q with integers p, q, q≠0. It is a topic at the advanced level in Arithmetic & Number Sense.
What is the formula for Rational Numbers?
The key formula is ℚ = {p/q}.
Where is Rational Numbers used in real life?
Real-world examples: Representing exact ratios such as 3/7 in engineering; Expressing repeating decimals as fractions.
What should I learn before Rational Numbers?
Make sure you are comfortable with Significant Figures, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Rational Numbers?
Assuming a long non-repeating-looking decimal is irrational. Check the pattern or the definition.
How can I practise Rational Numbers?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Rational Numbers?
Move on to Irrational Numbers next.
Related advanced topics in Arithmetic & Number Sense
- Repeating Decimals – Decimals with a repeating block are rational and convertible to fractions.
- Compound Interest – Interest earned on principal and past interest.
- Inverse Proportion – When one quantity doubles, the other halves.
- Irrational Numbers – Real numbers that cannot be written as a fraction, such as √2 and π.
- Real Numbers – All rational and irrational numbers; the continuous number line.
- Square Roots of Non-squares – Approximate or simplify surds like √50 = 5√2.