Page 10 - Maths Class 06

number into different periods by using either the Indian system of numeration or the International
system of numeration. But first let us learn about place value.

Place Value
The basis of the number system is place value. It is this place value which gives value to the number.

Definition : Place value of a digit in a given number is the value of the digit because of the place or the
position of the digit in the number.
Let us take a number, for example, 2,45,13,768.

Crores Ten-Lakhs Lakhs Ten-Thousands Thousands Hundreds Tens Ones

2 4 5 1 3 7 6 8

Here, The place value of 2 is 2,00,00,000 (two crore).
The place value of 4 is 40,00,000 (forty lakh).
The place value of 5 is 5,00,000 (five lakh).

The place value of 1 is 10,000 (ten thousand).
The place value of 3 is 3,000 (three thousand).
The place value of 7 is 700 (seven hundred).

The place value of 6 is 60 (sixty).
The place value of 8 is 8 (eight).

In words : Two crore forty-five lakh thirteen thousand seven hundred sixty-eight.
In figures : 2,45,13,768.
In expanded notation : 2,00,00,000 + 40,00,000 + 5,00,000 + 10,000 + 3,000 + 700 + 60 + 8
= 2 × 1,00,00,000 + 4 × 10,00,000 + 5 × 1,00,000 + 1 × 10,000 + 3 × 1000
+ 7 × 100 + 6 × 10 + 8 × 1

EXAMPLE 11. Write the place values of the coloured digits in each of the following:
(a) 370345 (b) 2479034 (c) 42371509
SOLUTION : (a) The place value of 7 in 370345 is 70,000.
(b) The place value of 2 in 2479034 is 20,00,000.
(c) The place value of 1 in 42371509 is 1,000.
EXAMPLE 12. Write the following numbers in expanded notation:

(a) 4,89,342 (b) 31,85,204 (c) 3,24,05,620
SOLUTION : (a) 4,89,342 = 4,00,000 + 80,000 + 9,000 + 300 + 40 + 2
(b) 31,85,204 = 30,00,000 + 1,00,000 + 80,000 + 5,000 + 200 + 4
(c) 3,24,05,620 = 3,00,00,000 + 20,00,000 + 4,00,000 + 5,000 + 600 + 20

Successor and Predecessor
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.

For example, The successor of 5,673 is 5,673 + 1 = 5,674
The successor of 99,999 is 99,999 + 1 = 1,00,000.
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