Approximation: An approximation is anything that is similar but not exactly equal to something else.
(i) Method of approximation for Addition & subtraction equation: Let us understand this method with an example:
Example. Find the approximate value of ‘x’ upto 3 digit:
4673.483 + 8494.867 – 7526.461 = x – 894.356 + 143.793
(a)2200.698(b) 4860.564 (c) 6500.699 (d) 3886.648
Step 1: Convert the exact values into approximate values.
4673.483

4700, 8494.867

8500, 7526.461

7500, 894.356

900, 143.793

100
Step 2: Put the value approximate values in the equation
4700 + 8500 – 7500 = x – 900 + 100
Step 3: After solving the equation
x = 6500
6500 is the approximate value of x. So, option(c) is very near about 6500.
(ii) Method of approximation for multiplication & Division equation: Let us understand this method with an example:
Example: What is the approximate value nearly to ‘x’?
89487

124 x 19808

594 x 40238

873 = x?
(a)1086888 (b) 1857122(c) 80388 (d) 549534
Step 1: Convert the exact values into approximate values.
89487

89500, 124

125, 19808

19800, 594

600,
40238

40250, 873

875
Step 2: Put the approximate values in the equation.

Step 3: After solving the equation
x = 1086888.
1086888 is the approximate value of x. So, option (b) is very near about 1086888.
(iii) Method of approximation for square roots & cube roots:
Example: What is the approximate value of ‘x’?

(a)44 (b) 76 (c) 56 (d) 34
Step 1: Put the approximate values near the square root and cube root of an equation.
5342.04

5329,
5013.036

4913, 5847


, 7734

, 10649.876

10648.
Step 2: Put the value approximate values in the equation.
Step 3: After solving the equation
x = 73 + 17-18+4
x = 76.
Note: To get the result very near about the exact answer we should always decrease or increase some quantities to make the balance.
We have discussed concepts of Simplification and Approximation techniques in our article.
Hope this was helpful
All the best!!!