Number
Grade 3-5Estimation
Estimation questions ask for a quick, sensible approximation rather than an exact answer, and the method is always the same: round every number to 1 significant figure first, then calculate. This lesson covers estimating multiplications and divisions, estimating fraction-style calculations, and finding the whole numbers either side of a square root.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Estimating a calculation
Round every number in the calculation to 1 significant figure, then carry out the calculation with these rounded values. The result is an estimate, not the exact answer, so the working should always show the rounded numbers used.
312 × 48: round to 300 × 50, which gives an estimate of 15,000.
Estimating fraction-style calculations
When a calculation has a numerator and a denominator, round every number in both parts to 1 significant figure, then work out the resulting fraction.
(312 × 6.8) / 29: round to (300 × 7) / 30, which gives 2100 / 30 = 70.
Finding the whole numbers either side of a square root
To find which two consecutive whole numbers a square root lies between, find the square numbers directly below and above the number inside the root. The whole numbers being squared are the answer.
√130: 11² = 121 and 12² = 144. Since 130 lies between 121 and 144, √130 lies between 11 and 12.
Estimation in real-world problems
Word problems often describe a real quantity, such as a total cost or a total distance, and expect the same 1 significant figure rounding before multiplying or dividing.
A school has 587 students, each needing 1.9 exercise books: round to 600 × 2, giving an estimate of 1200 exercise books.
Worked Examples
Three exam-style questions, fully solved.
By rounding each number to 1 significant figure, estimate the value of 312 × 48.
Easy- 1.Round 312 to 1 significant figure: 300
- 2.Round 48 to 1 significant figure: 50
- 3.Multiply the rounded values: 300 × 50
Answer: 15,000
√130 lies between two consecutive whole numbers. Find these two numbers.
Medium- 1.Find a square number just below 130: 11² = 121
- 2.Find a square number just above 130: 12² = 144
- 3.Since 130 lies between 121 and 144, √130 lies between 11 and 12
Answer: 11 and 12
A school has 587 students and each student needs 1.9 exercise books. By rounding each number to 1 significant figure, estimate the total number of exercise books needed.
Hard- 1.Round 587 to 1 significant figure: 600
- 2.Round 1.9 to 1 significant figure: 2
- 3.Multiply the rounded values: 600 × 2
Answer: 1200 exercise books
Avoid These
The most common mistakes students make.
Rounding to a different number of significant figures than asked for, for example rounding to 2 significant figures instead of 1.
Calculating the exact answer first and then rounding the final result, instead of rounding each number before calculating.
In fraction-style estimates, rounding only the numerator or only the denominator, instead of rounding every number in the calculation.
When bounding a square root, picking square numbers that are not consecutive, instead of the two consecutive square numbers directly either side of the target number.
Forgetting to show the rounded numbers used in the working, which loses the method mark even if the final estimate is correct.
FAQ
Questions parents and students ask.
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