Round to a stated precision
Locate the place to keep. Use the next digit to decide and round directly from the original number
- Decimal places Count places after the decimal point. Zero decimal places means the nearest integer \(\displaystyle 12.684\approx12.68\quad(2\text{ d.p.})\)
- Significant figures Start at the first non-zero digit. Zeros between significant digits count \(\displaystyle 0.005086\approx0.00509\quad(3\text{ s.f.})\)
- Keep place value and precision Integer zeros preserve place value. The question supplies the significant-figure count. Final decimal zeros can state precision explicitly \(\displaystyle 47{,}283\approx47{,}000\quad(2\text{ s.f.})\)
- Negative numbers Round the magnitude and keep the sign. At an exact halfway value, choose the value farther from zero \(\displaystyle -3.85\approx-3.9\quad(1\text{ d.p.})\)
Common mistakes
Counting decimal places instead of significant figures
✕\(\displaystyle 0.08476\approx0.085\quad(3\text{ s.f.})\)✓\(\displaystyle 0.08476\approx0.0848\quad(3\text{ s.f.})\)
Count from the first non-zero digit. The incorrect answer has only two significant figuresDropping a required decimal zero
✕\(\displaystyle 6.097\approx6.1\quad(2\text{ d.p.})\)✓\(\displaystyle 6.097\approx6.10\quad(2\text{ d.p.})\)
The trailing decimal zero records hundredthsRounding twice
✕\(\displaystyle 3.749\approx3.75\approx3.8\)✓\(\displaystyle 3.749\approx3.7\quad(1\text{ d.p.})\)
The intermediate rounding changes the deciding digitDifficulty levels
introRound positive numbers to decimal places or significant figures without leading zeros
standardUse signed values, small decimals and zeros that preserve place value
challengeRound values involving carries, required zeros or exact halfway decisions
examSelect a rounded answer from alternatives based on common mistakes
Questions about this topic
Where do I start counting?+
For decimal places, start after the decimal point. For significant figures, start at the first non-zero digit
Why can the final zero matter?+
A final decimal zero can state the requested precision even though it does not change the value
Can I round in several steps?+
Round once from the original number. An intermediate rounding can change the deciding digit
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 1: Number and financial mathematics
In this chapter
Evaluate an integer expressionFactors, multiples, HCF, LCM and primesRound to decimal places or significant figuresEstimate an expression using rounded inputsConvert between fractions, mixed numbers and decimalsClassify real numbers and compare exact valuesAdd, subtract, multiply and divide fractions and mixed numbersWrite a ratio from countsWrite ratios in simplest formComplete equivalent ratiosUse a constant rateDivide a quantity in a given ratioDecide which option is the better valueConvert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1F Percentages and money: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changePercentage error against a reference value1G Percentage change and percentage error: Find the original amount from a percentageProfit, mark-up and discountIncome and taxSimple interestCompound interest (optional extension)