Represent the following decimal numbers pictorially.

**Representing a Decimal Number**

(i) Observe the following pictures which
represent tens, ones and tenths

For example, the decimal number 3.2 is
3 ones and 2 tenths that can be represented using the pictorial representations
as follows.

Similarly any decimal number can be represented
as above

**Try this**

**Represent the following decimal numbers pictorially.**

**(i) 5 ones and 3 tenths**

**(ii) 6 tenths**

**(iii) 7 ones and 9 tenths**

**(iv) 6 ones and 4 tenths**

**(v) Seven tenths**

We have studied about place value of
digits of a number in primary classes. Now let us extend our learning of place values
to decimal digits of a number. Let us recall the expanded form of a number. Consider
the number 3768.

The expanded form of 3768 is given by
3 × 1000 + 7 × 100 + 6 × 10 + 8 .

Now, let us consider a decimal number
235.68

Expressing the decimal number in the
expanded form, we get

235.68 = 200 + 30 + 5 + 6/10 + 8/100

=2×100 + 3×10 + 5×1 + 6×1/10 + 8 × 1/100

**Think**

The above expression can
also be expressed in terms of powers of 10 as follows 235.68 = 2 × 10^{2} + 3 × 10^{1} + 5 × 10^{0} + 6 × 10^{−}^{1} + 8 × 10^{−}^{2} . Hence, in any number,
when we move towards right from one digit to the next, the place value of a digit
is divided by 10^{1}.

Representing the two numbers 3768 and
25.6 in the place value grid, we get

In the beginning of this chapter, we
came across the discussion about the length of the pencils of Kavin and Kala. Those
lengths can also be represented in the place value grid as follows.

We know that the digit to the right of
ones place is known as tenths and the point is called decimal point which separates
the integral part and decimal part of a number.

In the above situation, we have expressed
numbers with one decimal digit in place value grid. Now to express numbers with
two decimal digits in place value grid, let us consider the example already discussed
in the introduction part.

Ravi has purchased dress materials for
pongal festival. The length of the pant material is 4* m *75 *cm*. To express the centimetre
in terms of metres, we proceed as follows.

We know that

100 *cm* =
1 *m*

1 *cm* =
1/100 *m*

Therefore one centimetre can be represented
as one hundredth of a metre.

Similarly, 75 *cm* =
75/100 =
0.75 *m*

So the length of the pant material is
4 +
0.75 *m*

That is 4.75 m. It can be read as four
and seventy five hundredth of a metre or four point seven five metres.

** Note**

The decimal digits of a
number have to be read as separate digits.

**Try these**

**1. Express the following decimal numbers in an expanded form and
place value grid form.**

**(i) 56.78**

The expanded form of 56.78 = 50+6 + 7/10 + 8/100

= 5 × 10 + 6 × 1 + 7 × 1/10
+ 8 ⊂ 1/100

Place value grid form

**(ii) 123.32 **

Expanded form of 123.32 = 100 + 20 + 3 + 3/10 + 2/100

= 1 × 100 + 2 × 10 + 3 × 1 + 3 × 1/10 + 2 ⊂ 1/100

Place value grid

**(iii) 354.56**

Expanded form of 354.56 = 300 + 50 + 4 + 5/10 + 6/100

= 3 × 100 + 5 × 10 + 4 × 1 + 5 × 1/10 + 6 ⊂ 1/100

Place value grid

**2. Express the following measurements in terms of metre and in decimal
form. One is done for you.**

**3. Write the following numbers in the place value grid and find the
place value of the underlined digits.**

(i) 36.__3__7

Place value grid

36.__3__7

The place value of 3 in 36.37 is Tenth.

(ii) 267.0__6__

Place value grid

267.0 __6__

The place value of 6 in 267.06 is Hundredth.

(iii) 0.__2__3

Place value grid

0.__2__ 3

The place value of 2 in 0.23 is Tenth.

(iv) 27.6__9__

Place value grid

27.6**9**

The place value of 9 in 27.69 is Hundredth.

(v) 53.__2__7

Place value grid

53.** 2**7

The place value of 2 in 53.27 is Tenth.

Note that the tenth and hundredth place
values of a number can be written as 1/ 10 and 1/100 respectively.

__Example 1.1__** **Represent the following decimal
numbers pictorially.

(i) 0.3

(ii) 3.6

(iii) 2.7

(iv) 11.4

*Solution*

** **

__Example 1.2__** **Write the following in the
place value grid and find the place value of the** **underlined digits.

(i) 0.3__7__

(ii) 2.__7__3

(iii) 28.2__7__1

*Solution*

(i) The place value of 7 in 0.37 is Hundredth.

(ii) The place value of 7 in 2.73 is
Tenth.

(iii) The place value of 7 in 28.271
is Hundredth.

** **

** Example 1.3** The height of a person is 165

*Solution*

Since, 1 *cm*= 1/100* m *= 0.01 m

Given, height of the person = 165 *cm*.

Hence, the height of the person =
165 /100 = 1.65 m.

** **

__Example 1.4 __

Praveen goes trekking with
his friends. He has to record the distance in** **kilometres in his sports book. Can you help him?

The trekking record for four days are
given below

(i) 4 *m *

(ii) 28 *m *

(iii) 537 *m*

* *(iv)
3983 *m*

*Solution*

Since, 1 *m *= 1/1000* km *= 0.001 *km*

So, Praveen's trekking record is 0.004
*km*, 0.028 *km*, 0.537 *km*, 3.983 *km*.

** **

__Example 1.5 __

Express the numbers given
in expanded form in the place value grid. Also** **write its decimal representation.

*Solution*

Tags : Number System | Term 2 Chapter 1 | 7th Maths , 7th Maths : Term 2 Unit 1 : Number System

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7th Maths : Term 2 Unit 1 : Number System : Representing a Decimal Number | Number System | Term 2 Chapter 1 | 7th Maths

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