Approximation in Math

Approximation

Definition

• Approximation is the process of finding a value that is close to, but not exactly equal to, the actual value.
• It involves estimating a number or quantity to a certain degree of accuracy.

Types of Approximation

• Rounding off: approximating a number to the nearest ten, hundred, thousand, etc.
• Truncation: approximating a number by dropping digits beyond a certain point.
• Estimation by bounds: approximating a number by finding upper and lower bounds.

Rounding Off

• Rounding to the nearest whole number: approximating a decimal number to the nearest whole number.
• Rounding to a specific decimal place: approximating a decimal number to a specific number of decimal places.

Rules for Rounding Off

• If the digit to be dropped is 5 or greater, round up.
• If the digit to be dropped is 4 or less, round down.

Examples

• Approximate 43.7 to the nearest whole number: 44
• Approximate 12.456 to two decimal places: 12.46
• Approximate 75.89 to the nearest ten: 80

Approximation

Definition

• Approximation is a process of estimating a value to a certain degree of accuracy, which is close to, but not exactly equal to, the actual value.

Types of Approximation

• Rounding off: approximating a number to the nearest ten, hundred, thousand, etc.
• Truncation: approximating a number by dropping digits beyond a certain point.
• Estimation by bounds: approximating a number by finding upper and lower bounds.

Rounding Off

• Rounding to the nearest whole number: approximating a decimal number to the nearest whole number, by dropping the decimal part.
• Rounding to a specific decimal place: approximating a decimal number to a specific number of decimal places, by dropping digits beyond that point.

Rules for Rounding Off

• When rounding, if the digit to be dropped is 5 or greater, round up to the next digit.
• When rounding, if the digit to be dropped is 4 or less, round down to the previous digit.

Examples

• 43.7 ≈ 44 (rounded to the nearest whole number)
• 12.456 ≈ 12.46 (rounded to two decimal places)
• 75.89 ≈ 80 (rounded to the nearest ten)