Approximating whole numbers

Approximating whole numbers

Low and high approximation of whole numbers

The place value of a digit in the number is used in writing low or high approximation of the number. Low approximation of a number is done by adding 0 to the digit being approximated, while high approximation is obtained by adding 1 to the digit being approximated. When approximating a number, consider the place value of the digit at the right of the digit to be approximated.

Procedures for approximating whole numbers

1. If a digit to the right of the digit to be approximated is less than 5 (that is either 0, 1, 2, 3 or 4), add 0 to the digit being approximated and all digits which are on the right of the approximated digit will be replaced by 0.
2. If a digit on the right of a digit to be approximated is 5 or greater than 5 (that is 5, 6, 7, 8 or 9), add 1 to the digit being approximated and all digits on the right of the approximated digit will be replaced by 0.

Example 1

Approximate 3 459 210 to the nearest hundreds.

Solution

(a) The hundreds digit to be used in approximating the given number is 2.

(b) The digit on the right of 2 is 1, which is less than 5. According to procedure 1, add 0.

(c) Add 0 to the digit being approximated: 2 + 0 = 2.

(d) Write 2 in the position of hundreds, and all digits on its right (that is tens and ones) will be replaced by 0.

Therefore, the approximation of 3 459 210 to the nearest hundreds is 3 459 200. This is a low approximation, that is 3 459 210 ≈ 3 459 200.

Example 2

Approximate 2 323 478 to the nearest tens.

Solution

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

(b) The digit which is on the right of 7 is 8 which is greater than 5. According to procedure 2, add 1.

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

(d) Write 8 in the position of tens and all the digits on the right of 7 (ones) will be replaced by 0, that is 2 323 480.

Therefore, 2 323 478 ≈ 2 323 480 to the nearest tens. This is a high approximation.

Example 3

Approximate 8 759 601 to the nearest hundred thousands.

Solution

(a) The hundred thousands digit to be used in approximating the given number is 7.

(b) The 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 position of hundred thousands and all the digits on the right of 7 (ten thousands, thousands, hundreds, tens and ones) will be replaced by 0, that is 8 800 000.

Therefore, the approximation of 8 759 601 to the nearest hundred thousands is 8 800 000, that is 8 759 601 ≈ 8 800 000. This is a high approximation.