Estimate with rounded inputs
Replace each input by its one-significant-figure value, then preserve its grouping and operation order
- Round every input Start at the first non-zero digit, including for small decimals \(\displaystyle 0.074\approx0.07,\qquad59\approx60\)
- Keep the structure Brackets and fraction bars still group their contents after rounding \(\displaystyle \frac{8.3+1.6}{0.48}\approx\frac{8+2}{0.5}\)
- Stop after evaluating Only the inputs have been rounded unless the question gives another instruction \(\displaystyle 7\times40+3=283\)
- Check size An estimate can be higher, lower or equal to the exact result. It does not establish exact equality
Common mistakes
Rounding the exact result instead of the inputs
✕\(\displaystyle 4.2+8.7\times19=169.5\approx200\)✓\(\displaystyle 4.2+8.7\times19\approx4+9\times20=184\)
The instruction asks for every input to be rounded firstLosing the brackets
✕\(\displaystyle (3.6+2.3)\times7.4\approx4+2\times7=18\)✓\(\displaystyle (3.6+2.3)\times7.4\approx(4+2)\times7=42\)
The brackets group the addition in both expressionsUsing decimal places instead of significant figures
✕\(\displaystyle 0.037\approx0.0\quad(1\text{ s.f.})\)✓\(\displaystyle 0.037\approx0.04\quad(1\text{ s.f.})\)
Leading zeros do not count as significant figuresDifficulty levels
introEstimate a product with two positive inputs
standardEstimate a product with an added term or a bracketed sum multiplied by another input
challengeEstimate expressions with division and a grouped or separate addition
examChoose an estimate for grouped multiplication and division
Questions about this topic
Do I round the result as well?+
Only when asked. Here the instruction applies to each input, so evaluate the rounded expression and stop
Can an estimate be higher than the exact value?+
Yes. It can be higher, lower or equal. The operations and the changes to the inputs determine the effect
Why keep the brackets?+
Rounding changes the numbers, not the operations or their grouping
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)