Estimating Calculations (IGCSE Maths)
Estimating calculations means rounding every number to 1 significant figure and working the calculation out in your head, and it is a regularly examined skill on the Edexcel IGCSE Maths course. On this page you will learn how to round each value to 1 significant figure, how to estimate products, quotients, squares, square roots and fractions, and how to use an estimate to check whether an answer is sensible. Read the worked examples, then scroll down to the free auto-marked practice questions and try every question type for yourself.
How to Estimate a Calculation
An estimate is a quick, rough answer worked out without a calculator. You are not trying to be exact: you are trying to get close enough, fast enough, to know roughly what the real answer should be. The standard IGCSE method is always the same three steps.
- Round every number to 1 significant figure. Every number in the calculation, not just the awkward looking ones.
- Do the easy calculation. Keep the operations exactly as they were, including any brackets, powers and roots.
- Write the answer with the ≈ sign. The answer is an estimate, so it is approximately equal to the real value, not equal to it.
\( 38.6 \times 5.14 \approx 40 \times 5 = 200 \)
Rounding to 1 significant figure
The first significant figure is the first non-zero digit, counting from the left. Look at the digit straight after it: 5 or more rounds up, less than 5 rounds down. Every other digit becomes a zero (or disappears, after the decimal point).
| Number | First significant figure | Rounded to 1 s.f. |
|---|---|---|
| 6.83 | 6 | 7 |
| 412 | 4 | 400 |
| 27 480 | 2 | 30 000 |
| 0.0873 | 8 | 0.09 |
| 0.00214 | 2 | 0.002 |
Rounding to 1 significant figure on a number line
Core Ideas of Estimating Calculations
Worked Examples
💡 Example 1: a product
Estimate the value of \( 4.87 \times 61.3 \).
What's happening?
4.87 rounds to 5 and 61.3 rounds to 60. The multiplication is now easy: 5 × 6 = 30, then put the zero back. The exact answer is 298.531, so the estimate is very close.
💡 Example 2: a quotient
Estimate the value of \( 583.4 \div 18.7 \).
What's happening?
583.4 rounds to 600 and 18.7 rounds to 20. Dividing is now a one step calculation: 60 ÷ 2 = 30. The exact answer is 31.2 (3 s.f.).
💡 Example 3: a fraction
Estimate the value of \( \dfrac{39.2 \times 5.13}{9.6} \).
What's happening?
Round all three numbers to 1 s.f. first. Work out the top of the fraction, then divide. The fraction line does the dividing, so no extra brackets are needed.
💡 Example 4: a square root
Estimate the value of \( \sqrt{0.0873} \).
What's happening?
0.0873 rounds to 0.09, which is a square number in disguise: 0.3 × 0.3 = 0.09. A square root makes a small number bigger, so an answer larger than 0.0873 is expected here.
💡 Example 5: brackets and a power
Estimate the value of \( \big(6.9 \times (9.1 - 6.2)\big)^2 \).
What's happening?
The order of operations does not change: inside brackets first, then multiply, then square. Round each number separately: 6.9 rounds up to 7 while 9.1 and 6.2 both round down, to 9 and 6.
💡 Example 6: very large and very small numbers
Estimate the value of \( 0.0293 \times 61\,800 \), giving your answer in standard form.
What's happening?
Round to 1 s.f., then write each number in standard form. Now multiply the front numbers and add the powers of 10. Finally tidy 18 × 10² into standard form by moving one place: 1.8 × 10³, which is 1800.
💡 Example 7: estimating an area
A rectangular garden sign measures 22.6 cm by 4.13 cm. Estimate its area.
What's happening?
Round each measurement to 1 s.f., then use the area formula as normal. Estimating a measurement question is worth doing before you reach for the calculator: it tells you whether the number on the screen is believable.
💡 Example 8: using an estimate to check an answer
Tara works out \( 384 \times 19.6 \) on her calculator and writes down 75 264. Use an estimate to decide whether her answer is sensible.
75 264 is about 10 times bigger than 8000, so her answer is not sensible.
What's happening?
The estimate says the answer should be somewhere near 8000, and the real answer is 7526.4. Tara has almost certainly typed 196 instead of 19.6, which moves the decimal point one place and multiplies her answer by 10. This is exactly what estimating is for: you cannot spot a typing slip by staring at the calculator, but you can spot it against a rough answer you worked out yourself.
🔑 Key Points
- Every number gets rounded to 1 significant figure, including whole numbers such as 384 and numbers that already look easy.
- Keep the operations and brackets exactly as they are. Rounding changes the numbers, never the structure of the calculation.
- Choose the nearest square number when you estimate a square root: \( \sqrt{38.6} \approx \sqrt{36} = 6 \) is more useful than \( \sqrt{40} \).
- For very large or very small numbers, write each rounded value in standard form. Multiply the front numbers and add the powers of 10.
- Show the rounding line in the exam. Marks are given for the rounded calculation, not only for the final number.
⚠️ Common Pitfalls
- Working it out exactly and then rounding. That is not an estimate and it earns no marks. Round first.
- Counting the zeros in a small decimal as significant figures. In 0.00214 the first significant figure is the 2, so it rounds to 0.002.
- Rounding only some of the numbers, usually leaving the "easy" one alone.
- Losing a power of 10. Count the zeros carefully: \( 600 \div 20 = 30 \), not 3.
- Writing = instead of ≈ on the rounding line.
- Forgetting that dividing by a number below 1 makes the answer bigger: \( 20 \div 0.1 = 200 \).