## Approximation

Approximation is the value which is not equal to the exact result but is very close to the final result.
For example- If time is 7 : 58, and we say 8 : 00.
If you study 1 hour 55 minutes, and you say- I study 2 hours.

#### Basic Rules to Solve the Problems by Approximation

 Rule 1 :- To solve the complex mathematical expression, take the nearest value of numbers given in the expression.

For example - 33.333 is approximated to 33. Similarly, 69.8% is approximated to 70%.

Example- 125.009 + 69.999 + 104.989 = ?
Solution:- 125 + 70 + 105
≈ 300.

Example- 6885.009 - 419.999 - 94.989 = ?
Solution:- 6885 - 420 - 95
≈ 6370.

 Rule 2 :- To multiply large number, we can take the approximate value of numbers by increasing one number and decreasing the other.

For example - 249 × 101 is approximated 250 × 100 ≈ 25000.

Example- 36.98276421 × 21.00002 = ?
Solution:- 37 × 21
≈ 777 ≈ 775.

Example- 198.001 × 25 + 112.05 × 24.998 = ?
Solution:- 198 × 25 + 112 × 25
= 25 ( 198 + 112 ) = 25 × 310 = 7750.

 Rule 3 :- When we divide large number with decimals, then we can increase or decrease both numbers accordingly.

For example- 399.432 ÷ 40.002 is approximated as 400 ÷ 40 = 10.

Example- 49.0003 ÷ 74.999 = ?
Solution:- 50 ÷ 75

 = 50 = 2 = 0.653 ≈ 0.7. 75 3

Example- 840.003 ÷ 23.999 = ?
Solution:- 840 ÷ 24 { ∴ Taking approximation value of 23.999 ≈ 24 }

 = 840 = 210 = 35 24 6