Decimals — NSW Year 7 Maths
Numbers with a decimal point, from race times and prices to lengths in metres. Eleven subtopics and 220 practice questions, each with a fully worked solution, aligned to NESA outcome MA4-FRC-C-01.
Decimals in NSW Year 7
Decimals are numbers written with a decimal point, where each place to the right of the point is worth one tenth of the place before it. In Year 7, students compare and order decimals (including negative ones), switch between decimals and fractions, and become confident with all four operations, using written methods and quick estimates to check that an answer is sensible.
The eleven subtopics below begin with ordering decimals and linking them to fractions, then work through adding and subtracting, multiplying and dividing by powers of 10, multiplying and dividing decimals, terminating and recurring decimals and rounding, before finishing with worded problems. Decimals is one of the 13 topics in NSW Year 7 Maths and sits in the Number and Algebra strand (NESA outcome MA4‑FRC‑C‑01). These skills lead straight into percentages, money and measurement, and later into ratios and rates.
Subtopics
Decimals: common questions
What do students learn about decimals in Year 7?
Year 7 students compare and order decimals, convert between decimals and fractions, round to a set number of decimal places, and add, subtract, multiply and divide decimals with and without a calculator.
How do you multiply decimals?
Multiply the numbers as if there were no decimal points, then give the answer as many decimal places as the question has in total. For example, for \(0.3 \times 2.4\) work out \(3 \times 24 = 72\); there are two decimal places, so the answer is \(0.72\).
Why is \(0.25\) smaller than \(0.3\)?
Decimals are compared place by place from the left, not by how many digits they have. Writing \(0.3\) as \(0.30\) shows it is 30 hundredths, which is more than 25 hundredths.
Which NESA outcome covers decimals?
Decimals sit in Stage 4 of the NSW Mathematics K–10 Syllabus (2022) under outcome MA4‑FRC‑C‑01, usually taught in Year 7. Writing powers of 10 such as \(10^3\) also links to outcome MA4‑IND‑C‑01.
What comes after decimals in Year 7?
Fractions come next, and decimals are used again for percentages, money problems and measurement such as perimeter and area. Later in Stage 4 they appear in ratios, rates and data.