## 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

= | = | = 0.653 ≈ 0.7. | ||

75 | 3 |

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

= | = | = 35 | ||

24 | 6 |