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Hello our dear learners, today we are going to learn about approximation. Many of you might have doubts, so let&#39;s clear all your problems.

We use approximation in our daily life to ease down our day-to-day work. In mathematical expressions which include division and multiplication of decimal values of large numbers. It becomes quite complex to solve these problems, so to solve these we use approximation.

When we approximate the final result obtained is not equal to the exact result, but it is very close to the exact result.

Let’s try one.

E.g. ? = 32.01 + 128.01 × 1023.99 + 7.99

Sol: Solving by BODMAS rule, as learned earlier

? = 32.01 + 131,080.9599 + 7.99

? = 32.01 + 131,080.9599 + 7.99 = 131,120.9599

E.g. 10% of 1350 + ? = 365 

10/100 × 1350 + ? = 365

135 + ? = 365

? = 365 – 135

? = 230

E.g. 78 × 98 – 25% of 1376

78 × 98 – 25/100 × 1376

7644 – 34400/100 = 7644 – 344

7300 (it requires tedious calculation)

After this tedious calculation (128.01 × 1023.99) without a calculator, we are not left with time, in the exam hall we will prefer to leave this question.

In Approximation, to solve the complex mathematical expression, take the nearest value of numbers given in the expression. Try to make unit digit 0’ in most cases.

E.g. ? = 32.01 + 128.01 × 1023.99 + 7.99

Let’s try to round off to nearest integer

? = 32 + 128 × 1024 + 8

Or we can say,

? = 25 + 27 × 210 + 23

? = 25 + 217 + 23

? = 23 (22 + 214 + 1)

? = 8 (16389) = 131112

By calculator we would get 131112.09

Here it is, we got the solution.

E.g. 393 × 197 + 5600 × 5/4 + 8211.80 = ?

393 × 197 + 5600 × 5/4 + 8211.80 = ?

390 × 200 + 5600 × 5/4 + 8200 = ?

390 × 200 + 5600 × 5/4 + 8200 = ?

(By BODMAS rule)

390 × 200 + 7000 + 8200 = ?

78000 + 7000 + 8200 = 93200 (Ans.)

We got 92,632.8 by calculator. It is quite near its original value.

Tip: For finding 10% of a number simply move the decimal to one digit left.

For finding 25% simply divides the number by 4.

<h2>Short- cut method for percentage</h2>

<table cellspacing="0" class="Table" style="border-collapse:collapse; border:none; margin-left:27px; width:300px">
	<tbody>
		<tr>
			<td>
			Sr.

			No.
			</td>
			<td>
			Required Percentage

			(%)
			</td>
			<td>
			Number

			divided by
			</td>
		</tr>
		<tr>
			<td>
			1.
			</td>
			<td>
			200
			</td>
			<td>
			½
			</td>
		</tr>
		<tr>
			<td>
			2.
			</td>
			<td>
			50
			</td>
			<td>
			2
			</td>
		</tr>
		<tr>
			<td>
			3.
			</td>
			<td>
			33.33
			</td>
			<td>
			3
			</td>
		</tr>
		<tr>
			<td>
			4.
			</td>
			<td>
			25
			</td>
			<td>
			4
			</td>
		</tr>
		<tr>
			<td>
			5.
			</td>
			<td>
			20
			</td>
			<td>
			5
			</td>
		</tr>
		<tr>
			<td>
			6.
			</td>
			<td>
			10
			</td>
			<td>
			10
			</td>
		</tr>
		<tr>
			<td>
			7.
			</td>
			<td>
			5
			</td>
			<td>
			20
			</td>
		</tr>
		<tr>
			<td>
			8.
			</td>
			<td>
			1
			</td>
			<td>
			100
			</td>
		</tr>
	</tbody>
</table>

E.g. 10% of 1350 + ? = 365

? = 365 – 10% of 1350

? = 365 – 135.0 = 230.0 (Ans).

E.g. 78 × 98 – 25% of 1376

78 × 98 – 344 (Using approximation and table)

8000 – 344 = 7656 (Ans.)

This can be done in mind without the use of pen and paper.

E.g. 34.02% of 550.09 + ? = 297.07 + √728.95

34.02% of 550.09 + ? = 297.07 + √728.95

34% of 550 + ? = 300 + √729

(25 + 10 – 1)% of 550 + ? = 300 + 27

25% of 550 + 10% of 550 – 1% of 550 + ? = 327

137.5 + 55 – 5.5 + ? = 327

132 + ? = 327

? = 327 – 132 = 195 (Ans.)

E.g. (? + 9.97) × 12.8 = 20.12% of 1319.97

(? + 10.00) × 13.0 = 20.00% of 1320.00

(Using approximation)

(? + 10.00) × 13.0 = 1/5 × 1320.00

(? + 10.00) × 13.0 = 264 

(? + 10.00) = 260/13

(Using approximation) 

? = 20 – 10 = 10 (Ans.)

Hope your doubts are clear. Practice some more questions for better understanding of this topic and stay connected.

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