Approximation of decimals

Approximation of decimals

Decimal places are read towards the right after a decimal point. Approximation of decimals is done according to the given number of decimal places.

Procedures for approximating decimals

There are two procedures to be considered when approximating decimals.

1. If the digit to the right of the digit to be approximated is less than 5, add 0 to the digit being approximated. That is, leave the digit unchanged. Then, all the digits on the right of the approximated digit will be replaced by 0, which are usually not written.

Example

Approximate 9.0347 to two decimal places.

Solution

(a) The digit to be used in approximating the given number to two decimal places is 3.

(b) The digit which is on the right of 3 is 4 which is less than 5.

According to procedure 1, add 0.

(c) Add 0 to the digit being approximated: 3 + 0 = 3.

(d) Write 3 in the second decimal place and all digits on the right of 3 will be replaced by 0, which are usually not written.

Therefore, the approximation of 9.0347 to two decimal places is 9.03, that is 9.0347 ≈ 9.03

Example 2

Approximate 10.2571 to three decimal places.

Solution

(a) The digit to be used in approximating the given number to three decimal places is 7.

(b) The digit which is on the right of 7 is 1 which is less than 5. By considering procedure 1, add 0.

(c) Add 0 to the digit being approximated: 7 + 0 = 7.

(d) Write 7 to the third decimal place, and all digits on the right of 7 will be replaced by 0, which is not written, that is 10.257.

Therefore, the approximation of 10.2571 to three decimal places is 10.257, that is 10.2571 ≈ 10.257.

2. If the digit on the right of the digit to be approximated is 5 or greater than 5, add 1 to the digit being approximated. All other digits on the right of the approximated digit will be replaced by 0, which is not written.

Example 3

Approximate 0.4763 to one decimal place.

Solution

(a) The digit to be used in approximating the given number to one decimal place is 4.

(b) The digit which is on the right of 4 is 7 which is greater than 5; by considering procedure 2, add 1.

(c) Add 1 to the digit being approximated: 4 + 1 = 5.

(d) Write 5 in the first decimal place, and all the digits on the right of 4 will be replaced by 0, which is usually not written.

Therefore, the approximation of 0.4763 to one decimal place is 0.5, that is 0.4763 ≈ 0.5

Example 4

Approximate 5.07523 to two decimal places.

Solution

(a) The digit to be used for approximating this number to two decimal places is 7.

(b) The next digit to the right of 7 is 5.

(c) The digit to be approximated is 7. According to procedure 2, add 1.

(d) Add 1 to the digit being approximated 7 + 1 = 8.

(e) Write 8 in the second decimal place, and all the digits on the right of 7 will be replaced by 0, which is not written.

Therefore, the approximation of 5.07523 to two decimal places is 5.08, that is 5.07523 ≈ 5.08.