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!!!