Decimals

1. Decimal Notation:

(i) To understand the parts of one whole (i.e. a unit) we represent a unit by a block. One block divided into $10$ equal parts means each part is 110 (one-tenth) of a unit. It can be written as $0.1$ in decimal notation.

(ii) The dot represents the decimal point and it comes between the units place and the tenths place.

(iii) Every fraction with denominator $10$ can be written in decimal notation and vice-versa.

(iv) One block divided into $100$ equal parts means each part is 1100 (one-hundredth) of a unit. It can be written as $0.01$ in decimal notation.

(v) Every fraction with denominator $100$ can be written in decimal notation and vice-versa.

2. Place Value:

(i) In the place value table, as we go from left to the right, the multiplying factor becomes 110 of the previous factor.
(ii) The place value table can be further extended from hundredths to 110 of hundredths i.e. thousandths 11000, which is written as $0.001$ in decimal notation.

3. Comparison of Decimals:

(i) All decimals can also be represented on a number line.

(ii) Every decimal can be written as a fraction.

(iii) Any two decimal numbers can be compared among themselves. The comparison can start with the whole part. If the whole parts are equal, then the tenth parts can be compared and so on.

4. Application of Decimals:

Decimals are used in many ways in our lives. For example, in representing units of money, length, and weight.