Free Year 9 Rational and irrational numbers Practice | Skillo
Year 9 students sitting their final NAPLAN need to be confident with rational and irrational numbers. Recognise that the real number system includes the rational numbers and the irrational numbers. Skillo has targeted practice questions for this exact skill, mapped to the Australian Curriculum v9.0, free and ready to go.
Start Free Practice →What is tested: Rational and irrational numbers
- ✓Recognise that the real number system includes the rational numbers and the irrational numbers.
- ✓Questions may include word problems set in real Australian contexts
- ✓Both calculator and non-calculator question types are covered
Sample questions
Question 1 — Easy
Australia's national debt at a particular point in time was reported as $9.04 × 10¹¹ dollars. Mei wants to convert this amount into standard decimal form to include in her economics project. Which of the following correctly represents this value as a standard decimal?
Answer: To convert 9.04 × 10¹¹ to a standard decimal, move the decimal point 11 places to the right: 9.04 becomes 904,000,000,000, which is 904 billion dollars. Option A moves only 9 places. Option C moves only 10 places. Option D moves 12 places, which overstates the value by a factor of 10.
Question 2 — Medium
The Great Barrier Reef covers an area of approximately 344,400 square kilometres. Priya is writing a report and needs to express this area in scientific notation to 3 significant figures. Which of the following correctly represents this value in scientific notation?
Answer: 344,400 written in scientific notation requires moving the decimal point 5 places to the left, giving 3.444 × 10⁵. Rounded to 3 significant figures, this is 3.44 × 10⁵ km². Option B has 4 significant figures, not 3. Option C is not in standard form because the coefficient must be between 1 and 10. Option D uses the wrong exponent — 10⁶ would represent a number in the millions.
Question 3 — Hard
A marine biologist studying whale migration records that a humpback whale travels approximately 1.68 × 10⁴ kilometres each year during its migration. Zac calculates that the same whale would travel this distance for 250 years. What is the total distance in standard form, expressed to 3 significant figures?
Answer: The total distance is 1.68 × 10⁴ × 250. First, 1.68 × 250 = 420, and 420 × 10⁴ = 4.20 × 10⁶ km. This is already in scientific notation to 3 significant figures. Option B uses an incorrect exponent of 5. Option C incorrectly uses an exponent of 7. Option D transposes the digits in the coefficient, giving 4.02 instead of 4.20.
How to use Skillo for Year 9 Numeracy
- Select Year 9 and Numeracy on the home screen
- Use Quick Practice — questions on rational and irrational numbers will appear as part of the session
- Check the Skill Breakdown on your profile to track your accuracy on rational and irrational numbers specifically
- Review explanations after each question to understand the reasoning behind correct answers
Skillo is free, requires no email or account details, and is built specifically for Australian students. Every question is mapped to the Australian Curriculum v9.0 and filtered by skill so your child practises exactly what they need.
No account needed. No email. No credit card.