## What is a Decimal Value and Place Value of Decimals

Decimal Fractions
Introduction
Riya, Nutan, and Roshan are studying in the same class. In the mathematics examination, marks obtained by Riya and Nutan are 72 and 78 respectively, but the marks obtained by Roshan is 80.5.

Children, do you know the meaning of 80.5 ? It is nothing but $$80\frac{1}{2}$$. $$\frac{1}{2}$$ can also be written as 0.5.
0. 5 is the decimal representation of fraction $$\frac{1}{2}$$. A decimal number is a number that contains a decimal point.
We know that the place value of a digit increases 10 times as it moves one step towards the left or decreases $$\frac{1}{10}$$ times as it moves one step towards the right. Watch the place value of digits in the Table.

### Decimal Fractions

Let us consider a square divided into ten equal parts, then each part of the square will represent one-tenth $$(\frac{1}{10})$$ of the whole square. The decimal form of one-tenth is 0.1 read as ‘zero decimal one’ or ‘zero point one’; The fractional form of one tenth is $$(\frac{1}{10})$$

When we divide a square into 100 equal parts, then each part of square represents $$(\frac{1}{100})$$, which is called
‘one hundredth’ and can be written in the decimal form as 0.01.
Note: The word ‘DECIMAL’ means ‘based on 10’. This word is derived from the latin word decima meaning – a tenth part.

Similarly, if we divide a square into 1000 equal parts, then each part will be represented by $$(\frac{1}{1000})$$ called ‘one-thousandth’ and written as 0.001 in decimal form.
From the above, it is clear that

Hence, fractions with denominators 10,100,1000, etc. are known as decimal fractions or simply decimals. A decimal consists of two parts separated by a decimal point (•)
(i) Whole number part
(ii) Decimal part.
The digits, which are to the left side of a decimal point are called whole number part and the digits which are to the right side of a decimal point are called decimal part.
Example

While reading a decimal fraction, the digits on the left of the decimal point are read as whole number and the digits on the right of the decimal point are read as individual digits.
Example: 625.314 can be read as six hundred twenty-five point three one four.
22.768 = twenty-two point seven six eight.
Observe the following:

Note:
If there is no whole number part in a decimal number then write 0 on the left of the decimal point.
Example: 0.67, 0.132, 0.5, etc
Writing decimals in place value chart
Table given on the next page shows the value of each place in a decimal fraction.
We can use this place value chart to expand a decimal fraction using decimals or fractions.

### Expanded Form

This is a form, in which we add the place value of each digit forming the number.

Decimal places: The number of digits contained in the decimal part of a decimal fraction gives the number of decimal places.

## What is the meaning of Place Value and Face Value in Maths

### Place value and face value:

The place value of a digit of a number depends upon its position in the number. The face value of a digit of a number does not depend upon its position in the number. It always remains the same wherever it lies regardless of the place it occupies in the number.

Example: Let us see the place value and face value of the underlined digit in the number 1,32,460. The digit 2 in the number 1,32,460 lies in the thousands period (1000) and hence the place value of 2 is 2 thousands (or 2000). The face value of 2 is 2 only.

### Expanded form:

When a number is written as the sum of the place values of all the digits of the number, then the number is in its expanded form.

Example: The expanded form of 9,67,480 is as shown below:
9,67,480 = 900000 + 60000 + 7000 + 400 + 80 + 0

Successor: The successor of a given number is the number that just succeeds it, i.e., ‘the number just after’ the given number. It is obtained by adding one (1) to the given number.

Examples

• The successor of 5,678 is 5,678 + 1 = 5,679.
• The successor of 99,999 is 99,999 + 1
= 1,00,000.

Predecessor: The predecessor of a given number is the number that just precedes it, i.e. ‘the number just before’ the given number. It is obtained by subtracting one (1) from the given number.

Examples

• The predecessor of 1,257 is 1,257 – 1 = 1,256.
• The predecessor of 1,00,000 is 1,00,000 – 1
= 99,999.