Approximation Questions: How to Round and Pick the Answer
Round awkward numbers safely, calculate, and pick the nearest option. Six original questions show how.
An approximation question gives you awkward numbers like 24.97, 39.89% or √1023.8 and asks for the value closest to the answer. You are not meant to calculate the exact figure. You round each number to a friendly one, calculate, and pick the nearest option.
The skill is knowing how far you can round without moving the answer past the next option. The options are usually spread out, which is why rounding works.
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What Each Number Usually Rounds To
24.97, 16.02
Round to
25, 16
Why it is safe
The change is less than 0.2% of each number
39.89% of 650.3
Round to
40% of 650
Why it is safe
Percentages near a round figure become easy fractions (40% = 2/5)
√1023.8
Round to
32
Why it is safe
1024 is a perfect square, 32²
∛3374.6
Round to
15
Why it is safe
3375 is a perfect cube, 15³
299.8 ÷ 9.98
Round to
300 ÷ 10
Why it is safe
Both moved by a tiny amount in the same direction
| You see | Round to | Why it is safe |
|---|---|---|
| 24.97, 16.02 | 25, 16 | The change is less than 0.2% of each number |
| 39.89% of 650.3 | 40% of 650 | Percentages near a round figure become easy fractions (40% = 2/5) |
| √1023.8 | 32 | 1024 is a perfect square, 32² |
| ∛3374.6 | 15 | 3375 is a perfect cube, 15³ |
| 299.8 ÷ 9.98 | 300 ÷ 10 | Both moved by a tiny amount in the same direction |
The Method
- 1
1. Look at the options first
If the options are far apart, round boldly. If two are close, round less and keep one decimal.
- 2
2. Round each number to the nearest friendly value
Whole numbers, multiples of 5 or 10, perfect squares and cubes, and percentages that are easy fractions.
- 3
3. Apply BODMAS to the rounded expression
The order of operations does not change because the numbers are rounded.
- 4
4. Pick the nearest option
Your answer will rarely match an option exactly. Choose the closest one.
Practice Questions With Full Solutions
Original questions written for this page. Each solution shows the rounded working and the exact check.
- 1
Practice question 1: 24.97 × 16.02 + 299.8 ÷ 9.98 ≈ ?
Round: 25 × 16 = 400, and 300 ÷ 10 = 30. So 400 + 30 = 430. Exact check: about 400.02 + 30.04 = 430.06. Answer: about 430.
- 2
Practice question 2: 39.89% of 650.3 + 14.92% of 399.7 ≈ ?
Round: 40% of 650 = 260, and 15% of 400 = 60. So 260 + 60 = 320. Exact check: about 259.4 + 59.6 = 319.0. Answer: about 320.
- 3
Practice question 3: √1023.8 × 6.98 − 19.99² ÷ 4.02 ≈ ?
Round: √1024 = 32, and 32 × 7 = 224. Then 20² = 400, and 400 ÷ 4 = 100. So 224 − 100 = 124. Exact check: about 223.3 − 99.4 = 123.9. Answer: about 124.
- 4
Practice question 4: 1199.7 ÷ 24.03 × 7.96 ≈ ?
Round: 1200 ÷ 24 = 50, and 50 × 8 = 400. Exact check: about 49.93 × 7.96 = 397.4. Answer: about 400.
- 5
Practice question 5: ∛3374.6 + 44.95 × 3.02 ≈ ?
Round: ∛3375 = 15, and 45 × 3 = 135. So 15 + 135 = 150. Exact check: about 15.0 + 135.7 = 150.7. Answer: about 150.
- 6
Practice question 6: (7.99 × 12.05 + 3.98) ÷ 4.97 ≈ ?
Round: 8 × 12 = 96, and 96 + 4 = 100. Then 100 ÷ 5 = 20. Exact check: about 100.26 ÷ 4.97 = 20.2. Answer: about 20.
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Common Traps
- check_circleRounding a large multiplier carelessly. Turning 47 × 18.6 into 50 × 20 adds about 126. If options are 100 apart, that is a wrong answer.
- check_circleRounding both numbers up in a product. The errors add together. Where you can, round one up and one down.
- check_circleRounding a divisor. Dividing by 4.5 as if it were 5 changes the answer by about 10%. Keep small divisors close to their real value.
- check_circleRounding a square before squaring it. 19.6² is about 384, not 400. Rounding inside a power grows the error.
- check_circleForgetting BODMAS. Rounded numbers still follow the same order of operations.
Approximation or Simplification?
If the numbers are clean (48, 3/4, √1764) the question wants the exact value: that is simplification. If they are slightly off (47.98, 39.89%, √1023.8) and the question says "approximately" or "≈", round first.
How Bank and SSC Papers Test This
In IBPS PO, approximation and simplification are listed together under Quantitative Aptitude. The prelims section has 35 questions for 30 marks within a 60-minute paper. In mains, Data Analysis & Interpretation (40 questions, 60 marks) rewards the same habit, because estimating figures in a data set is often faster than exact calculation.
IBPS Clerk and IBPS RRB list approximation in their Numerical Ability syllabus too. In SSC CGL, the Tier 1 Quantitative Aptitude section (25 questions, 50 marks) covers number system and simplification, where quick estimation helps you rule out options.
FAQs
How do you solve approximation questions quickly?expand_more
Check how far apart the options are, round every number to a friendly value, apply BODMAS, and pick the nearest option.
How much can I round in approximation questions?expand_more
If the options are far apart, round to the nearest whole number or multiple of 5. If two options are close, keep one decimal place and round less.
What is the difference between approximation and simplification?expand_more
Approximation asks for the nearest value and expects you to round. Simplification asks for the exact value and expects no rounding.
Which squares and cubes should I know for approximation?expand_more
Squares up to 30 and cubes up to 20. Numbers like 1023.8 or 3374.6 are usually placed next to a perfect square or cube on purpose.
Next steps
Take a full IBPS PO mock testThe whole syllabus, timed and scored, in one sitting.