Approximate Values
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Solved Examples
Study MaterialSolved Examples – Approximate Values
Solved examples help students understand the practical application of approximation, rounding off, estimation, and decimal simplification techniques in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, Insurance, Defence, CAT, CDS, NDA, and various aptitude examinations.
Topics Covered in Solved Examples
- Rounding Off Numbers
- Decimal Approximation
- Nearest Tens, Hundreds and Thousands
- Estimation Techniques
- Approximate Arithmetic Operations
- Approximate Fractions and Roots
- Competitive Exam Estimation
- Quick Mental Calculations
Example 1: Rounding to Nearest Ten
Question: Round off 348 to the nearest ten.
Solution:
Check the ones digit:
8 ≥ 5
Increase tens digit by 1.
348 ≈ 350
Answer: 350
Example 2: Rounding to Nearest Hundred
Question: Round off 473847 to the nearest hundred.
Solution:
Check tens digit:
4 < 5
Keep hundreds digit unchanged.
473847 ≈ 473800
Answer: 473800
Example 3: Rounding to Nearest Thousand
Question: Round off 875623 to the nearest thousand.
Solution:
Check hundreds digit:
6 ≥ 5
Increase thousands digit by 1.
875623 ≈ 876000
Answer: 876000
Example 4: Rounding to Nearest Lakh
Question: Round off 472804 to the nearest lakh.
Solution:
Check ten-thousand digit:
7 ≥ 5
Increase lakh digit by 1.
472804 ≈ 500000
Answer: 500000
Example 5: Decimal Approximation
Question: Approximate 2.456 correct to two decimal places.
Solution:
Check third decimal digit:
6 ≥ 5
Increase second decimal digit by 1.
2.456 ≈ 2.46
Answer: 2.46
Example 6: Decimal to One Decimal Place
Question: Approximate 32.89 correct to one decimal place.
Solution:
Check second decimal digit:
9 ≥ 5
Increase first decimal digit by 1.
32.89 ≈ 32.9
Answer: 32.9
Example 7: Approximate Multiplication
Question: Estimate:
198 × 49
Solution:
Approximate:
198 ≈ 200
49 ≈ 50
Estimated value:
200 × 50
= 10000
Answer: 10000
Example 8: Approximate Division
Question: Estimate:
998 ÷ 49
Solution:
Approximate:
998 ≈ 1000
49 ≈ 50
Estimated value:
1000 ÷ 50
= 20
Answer: 20
Example 9: Approximate Square Root
Question: Estimate:
√48
Solution:
Nearest perfect square:
49
√49 = 7
Therefore:
√48 ≈ 7
Answer: 7
Example 10: Approximate Cube Root
Question: Estimate:
∛28
Solution:
Nearest perfect cube:
27
∛27 = 3
Therefore:
∛28 ≈ 3
Answer: 3
Example 11: Approximate Fraction
Question: Estimate:
49/98
Solution:
Approximate:
49 ≈ 50
98 ≈ 100
Estimated fraction:
50/100
= 1/2
Answer: 1/2
Example 12: Approximate Addition
Question: Estimate:
498 + 203
Solution:
Approximate:
498 ≈ 500
203 ≈ 200
Estimated value:
500 + 200
= 700
Answer: 700
Example 13: Approximate Subtraction
Question: Estimate:
1002 − 497
Solution:
Approximate:
1002 ≈ 1000
497 ≈ 500
Estimated value:
1000 − 500
= 500
Answer: 500
Example 14: Decimal Approximation to Integer
Question: Approximate 2.99 to nearest integer.
Solution:
Decimal part:
0.99 ≥ 0.5
Increase integer part by 1.
2.99 ≈ 3
Answer: 3
Example 15: Approximate Decimal Fraction
Question: Approximate 20.093 correct to one decimal place.
Solution:
Check second decimal digit:
9 ≥ 5
Increase first decimal digit by 1.
20.093 ≈ 20.1
Answer: 20.1
Important Exam Tips
- Always identify required place value first.
- Use nearest easy numbers for estimation.
- Practice decimal rounding regularly.
- Use approximation for quick calculations.
- Avoid lengthy exact calculations.
- Improve mental estimation speed.
- Practice previous year aptitude questions.
Common Mistakes to Avoid
- Checking wrong digit during rounding.
- Ignoring decimal approximation rules.
- Incorrectly increasing previous digit.
- Using exact values unnecessarily.
- Rounding too early in calculations.
Practicing solved examples regularly improves conceptual clarity, estimation speed, and logical analysis in solving Approximate Values aptitude questions in competitive examinations.