Working with Numbers — NSW Year 8 Maths
Integers, decimals, powers, prime factors and the index laws. Twelve subtopics and 240 practice questions, each with a fully worked solution, aligned to NESA outcomes MA4-INT-C-01, MA4-FRC-C-01 and MA4-IND-C-01.
Working with Numbers in NSW Year 8
Working with Numbers sharpens the number skills that algebra, equations and measurement depend on. In Year 8, students use all four operations with negative integers and decimals, take recurring decimals further, meet irrational numbers and use prime factors and index notation to write numbers compactly and to simplify powers without a calculator.
The twelve subtopics below begin with adding, subtracting, multiplying and dividing integers and the order of operations, move on to decimals, terminating and recurring decimals, powers and roots, prime factors and the index laws, and finish by sorting rational and irrational numbers. Working with Numbers is one of the 14 topics in NSW Year 8 Maths and sits in the Number and Algebra strand (NESA outcomes MA4‑INT‑C‑01, MA4‑FRC‑C‑01 and MA4‑IND‑C‑01). These skills feed straight into algebra and Pythagoras' theorem, and in Stage 5 into scientific notation and surds.
Subtopics
Working with Numbers: common questions
What number skills are taught in Year 8 maths?
Year 8 extends Year 7 work on integers and decimals to longer calculations with negative numbers, recurring decimals and powers. It adds prime factors in index form, the index laws with numerical bases, and the difference between rational and irrational numbers.
What are the index laws?
When the bases are the same, multiply powers by adding the indices and divide them by subtracting, so \(2^9 \div 2^3 = 2^6\). A power of a power multiplies the indices, so \((7^3)^5 = 7^{15}\), and any non-zero number to the power 0 equals 1.
What is the difference between a terminating and a recurring decimal?
A terminating decimal stops, like \(\frac{7}{8} = 0.875\). A recurring decimal repeats a block of digits forever, like \(\frac{6}{7} = 0.\dot{8}5714\dot{2}\), where the block 857142 repeats. A fraction in simplest form terminates only when its denominator has no prime factors other than 2 and 5.
Which NESA outcomes cover Working with Numbers?
This topic draws on three Stage 4 outcomes in the NSW Mathematics K–10 Syllabus (2022): MA4‑INT‑C‑01 for integers, MA4‑FRC‑C‑01 for decimals and rational numbers, and MA4‑IND‑C‑01 for powers, roots, prime factors and the index laws.
Is the square root of 2 rational or irrational?
It is irrational. \(\sqrt{2}\) cannot be written as a fraction of two integers, and its decimal, \(1.41421\ldots\), never ends or repeats. The square root of a whole number is irrational unless the number is a perfect square, so \(\sqrt{25} = 5\) is rational.