Sample Questions on Approximation

Q1. Approximate the value of 1.2 x 2.8 using rounding to one decimal place. 

Solution: 

To approximate, we can round each number to one decimal place: 1.2 ≈ 1.2 and 2.8 ≈ 2.8 Then, we can multiply: 1.2 x 2.8 ≈ 3.36 Therefore, 1.2 x 2.8 approximates to 3.4 when rounded to one decimal place.

Q2: Approximate the value of 0.75 ÷ 0.3 using rounding to two decimal places. 

Solution: 

To approximate, we can divide 0.75 by 0.3 using a calculator and round the answer to two decimal places: 0.75 ÷ 0.3 ≈ 2.50 Rounded to two decimal places, 2.50 ≈ 2.50. Therefore, 0.75 ÷ 0.3 approximates to 2.50 when rounded to two decimal places.

Q3. Estimate the value of √(6.98 + 2.03). 

Solution: 

We can use the linear approximation, which gives us √(6.98 + 2.03) ≈ √7 + 1/14(2.03/√7) = 2.85. Therefore, the approximate value is 2.85.

Q4. Approximate the value of e^(-0.01). 

Solution: 

Using the Taylor series expansion of e^x, we have e^(-0.01) ≈ 1 – 0.01 + 0.005 = 0.995. Therefore, the approximate value is 0.995.

Q5. Estimate the value of ln(1.1). 

Solution: 

Using the linear approximation, we have ln(1.1) ≈ 0.1/1.1 = 0.0909. Therefore, the approximate value is 0.0909.

Q6. 235.8 ÷ 0.0032 + 12.6 × 4.9 = ? 

Solution: 

Using the order of operations, we perform the division first: (73500) + 12.6 × 4.9 =? Next, we perform the multiplication: (73500) + 61.74 =? Adding, we get: 73561.74 =? Therefore, the solution is 73561.74.

Q7. 75.002 × 1.98 – 89.997 + √(32.1 × 17.9) = ? 

Solution: 

Using the order of operations, we perform the multiplication first: (148.502) – 89.997 + √(574.59) =? Next, we perform the square root: (148.502) – 89.997 + 23.977 =? Adding and subtracting, we get: 82.482 =? Therefore, the solution is 82.482.

Q8. 15.996 × 7.998 + 18.002 ÷ 2.998 = ? 

Solution: 

Using the order of operations, we perform the multiplication first: (127.949008) + 18.002 ÷ 2.998 =? Next, we perform the division: (127.949008) + 6.006004 =? Adding, we get: 133.955012 =? Therefore, the solution is 133.955012.

Q9. √(16.003 × 23.998) – 12.997 × 1.998 + 31.999 ÷ 3.998 = ? 

Solution: 

Using the order of operations, we perform the multiplication first: √(384.023994) – 25.960006 + 8.000000 =? Next, we perform the square root: 19.599649 – 25.960006 + 8.000000 =? Adding and subtracting, we get: 1.639643 =? Therefore, the solution is 1.639643.

Q10. 43.999 ÷ 1.997 × 2.998 + 13.002 × 1.998 – 19.003 = ? 

Solution: 

Using the order of operations, we perform the division first: (44.0661) × 2.998 + 13.002 × 1.998 – 19.003 =? Next, we perform the multiplication: (132.023838) + 25.962996 – 19.003 =? Adding and subtracting, we get: 139.983834 =? Therefore, the solution is 139.983834.

Test your knowledge of Approximation in Quantitative Aptitude with the quiz linked below, containing numerous practice questions to help you master the topic:-

<<Practice Approximation Aptitude Quiz Questions>>

Approximation is a mathematical process that involves finding an estimate or approximation of a given value or expression. It is a valuable skill, particularly in Quantitative Aptitude tests, and is frequently used in competitive exams such as the SBI Clerk Mains, UPSC, PSC, and Railways. In fact, up to 10% of the total marks in these examinations may be dedicated to approximation questions. These questions are typically straightforward and can be solved quickly with a bit of practice. This article will provide an overview of approximation questions, their importance in competitive exams, and some tips and tricks for tackling them successfully. By the end of this article, you’ll have a better understanding of how to approach approximation questions and improve your chances of success in these exams.

Practice Quiz: 

Practice Approximation Aptitude Quiz Questions