By studying this lesson, you will be able to,

● recognize decimal numbers,

● compare decimal numbers and

● add decimal numbers having two decimal places.

13.1 Introduction to decimals

Each of the digits in a whole number occupies a place. We learnt about

this in the lesson on place value.

Let us now name the places occupied by the digits in each of 0.1, 0.2,

0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9.

Let us consider the number 0.5.

The figure below shows the place each digit in 0.5 occupies. These

places are indicated by squares.

Let us represent 2.5 using the abacus.

(1) Fill in the blanks of the table below.

(2) Write down the value represented by each abacus below.

(3) 

(a) Represent each of the numbers below on an abacus.

       (i) 0'7 (ii) 9'6 (iii) 9'9 (iv) 15'2

(b) Write down the value represented by each digit in each of the numbers given above.

Let us find the value represented by each digit of a number with two decimal places.

Let us consider the number 19.67.

The place of each digit in the number 19.67 is shown below. These are

indicated by squares.

Let us represent 19.67 on an abacus.

(4) The numbers below are given in words. Write them using digits.

(i) Zero point two one

(ii) One point one

(iii) Hundred and two point zero two

(iv) Seventeen point one seven

(v) Ten point eight five

(5) Complete the following table.

Let us now try to find the greater number from 0.7 and 0.5.

● Another method of comparing decimals

We can compare decimals using the values of its digits.

When comparing two decimal numbers the number having the greater

whole number part, is the greater number of the two. If both numbers

have the same whole number part, then we need to compare the digits

in their decimal places.

Then the number having the greater digit in the first decimal place is

the greater number of the two. If both numbers have the same digit in

the first decimal place, then we need to compare the digits in the second

decimal place. Then the number having the greater digit in the second

decimal place is the greater number of the two.

Let us explain this addition using the following steps.

(2) The electricity consumption of a household in the first two weeks

of last month was 45.7 units. The electricity consumption in the last

two weeks was 50.3 units. What is the total electricity consumption

during the last month?

Find the value of 3.65 - 1.98.

Let us explain this subtraction using the following steps.

(2) Nimal and Sunil inherited 0.75 of the total land owned by their father. If Nimal inherited 0.48 of the total land, how much of the land did Sunil inherit?

(3) A reservoir was filled to 0.7 of its total capacity. 0.15 of its total capacity was used to produce electricity. Of the total capacity, how much water is now left in the reservoir?