Approximation

We know that the digits of a number, one by one in order from left to right decrease in value rapidly.

Let us illustrate it by examples.

Mass of a gold ornament is 23.473 g. Round off to

(i) two decimal places, (ii) one decimal place.

23.473 g = (2 x 10) + (3 x 1) +

The successive digits from left to right decrease in value rapidly.

(i) 3^rd decimal place is less than 5,

We merely omit it.

23.473 g = 23.47g corrected to two decimal places

(ii) 2^nd decimal place is 7.

If it is 5 or more than 5, we increase 1^st decimal place by one.

23.473 g = 23.5 g corrected to one decimal place.

Write 9847.982 corrected to

(i) one decimal place (ii) integer (iii) hundred (iv) thousand

(i) 9848.0 2^nd d.p. is 5 or more than 5 [ 8 ]

1^st d.p. is increased by 1

(ii) 9848 1^st d.p. is 5 more than 5 [ 9 ]

unit's place is increased by 1.

(iii) 9800 ten's place is less than 5 [4]

we write 0 at unit's and ten's place.

(iv) 10,000 hundred's place is 5 or more than 5 [ 8 ]

thousands' place is increased by 1.

9 increases to 10 and in unit's, ten's and hundred's place we write 0.

[ i.e., 0 in the place of all digits to the right ]