When, How much and How to Approximate

An approximation is anything close but not exactly equal to something else. It is an important technique that helps a candidate find the solution quickly in competitive exams by rounding off to the nearest integer rather than solving the exact values.

You can understand the value and concept of this technique better with the help of the following examples:

Example 1:

Find the approximate value of (13.001)3.

1. 1900     2. 2200     3. 2000     4. 1800     5. 2100

Solution:

13.001 is approximately equal to 13. So, instead of finding the cube of 13.001, we can simply find the cube of 13 and tick the answer nearest to that value. Now, the cube of 13 is 2197, and in options, we have 2200, which is nearest to 2197, so the correct answer is the second option.

NOTE: Always check the options; if the gap between the options is quite significant, then an approximation can be made even if it is not mentioned in the question.

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Example 2:

What should replace the question mark in the following equation?

55.003 × 54.998 + 5.001 =?

1.3500     2. 3630     3. 2540     4. 3030     5. 2750

Solution:

55.003 is approximately equal to 55 as well as 54.998 is also approximately equal to 55.  At the same time, 5.003 is close to 5.

So, the equation reduces to the form 55 × 55 + 5 = 3025 + 5 = 3030. Besides, this question can also be solved by the algebraic formula. As you can write 55 × 55 + 5 = (50 + 5) × (50 + 5) + 5.

So, (50 + 5)2 + 5 = (502 + 52 + 2 × 5 × 50) + 5 = (2500 + 25 + 500) + 5 = 3025 + 5 = 3030.

Example 3:

What will 50.001% of 99.99 ÷ 49.999 be equal to?

1. 1     2. 0.1     3. 0.01     4. 0.02     5. None of these.

Solution:

50.001 is approximately equal to 50.

99.99 can be written as equivalent to 100, and 49.99 is equivalent to 50.

So the equation now becomes 50% of 100 ÷ 50 =?

50% of 100 is 50, and 50 divides by 50 answers 1.

Example 4:

999.001 + 899.99 –349.88 = ?

1. 1549     2. 1560     3. 1449     4. 1460     5. 1649

Solution:

Approximating the above equation, we get, 1000 + 900 – 350 = 1550

Option a is nearest to our answer. So, the correct answer is 1549.

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Example 5:

119% of 1190 + 33% of 125 – 97 % of 813 = ?

1. 620     2. 700     3. 725     4. 625     5. 675

Solution:

To find 119% of 1190

(100 + 19)% of 1190 so, 100 % of 1190 + 20 % of 1190

1190 + 238 = 1428

33 % of 125 (33% is equivalentto one-third) so, 125 × 1/3 = 42 approximately.

97% of 813 = (100% - 3%) of 813 = 813 – 24 = 789

Now, the final solution will be 1428 + 42 -789 = 1470 – 789 = 681

Answer nearest to our value is option 5.
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