Page 13 - Start Up Mathematics_6

Example 5: Insert commas suitably and write the number names according to International system
of numeration:

(a) 78921301 (b) 7452283 (c) 148049831
Solution:
Number Number with Number name
commas

(a) 78921301 78,921,301 Seventy-eight million nine hundred twenty-
one thousand three hundred one
Seven million four hundred fifty-two thousand
(b) 7452283 7,452,283 two hundred eighty-three

One hundred forty-eight million forty-nine
(c) 148049831 148,049,831 thousand eight hundred thirty-one

Example 6: Write the following numbers in expanded form:

(a) 3,45,892 (b) 6,90,39,283
Solution: (a) 3,45,892 = (3 × 1,00,000) + (4 × 10,000) + (5 × 1,000) + (8 × 100) + (9 × 10)
+ (2 × 1)

(b) 6,90,39,283 = (6 × 1,00,00,000) + (9 × 10,00,000) + (0 × 1,00,000)
+ (3 × 10,000) + (9 × 1,000) + (2 × 100) + (8 × 10) + (3 × 1)

Example 7: Find the difference between the place values of two 5s in 4,65,73,89,507.
Solution: The place value of 5 at crores place = 5,00,00,000

The place value of 5 at hundreds place = 500
The difference between the two place values = 5,00,00,000 – 500 = 4,99,99,500.

Hence, the required difference in place values of two 5s is 4,99,99,500.
Example 8: How many six-digit numbers are there in all?

Solution: To find the number of six-digit numbers, we need to know the largest and smallest
six-digit numbers.
Largest six-digit number = 9,99,999
Smallest six-digit number = 1,00,000
Total number of six-digit numbers = 9,99,999 – 1,00,000 + 1 = 9,00,000
Hence, there are 9,00,000 six-digit numbers in all.

Comparison of Numbers
In our previous classes, we have done comparison of small numbers, arranging the numbers in
ascending and descending orders and finding the greatest or smallest amongst them. Now let’s
see how to compare bigger numbers.

Procedure:
Step 1: First check the number of digits in the given numbers. The number having less number
of digits is always smaller than the number having more number of digits.
Step 2: If the number of digits are same in the given numbers, then start comparing the digits
from the extreme left of the given numbers.

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