Page 99 - Ganit Kaushal

Summary of the Chapter

• Indian System of Numeration: In the Indian system of numeration, we use ones, thousands, lakhs, and
crores as periods. In this system, a number is split up into groups or periods.

– The first period consists of ones, tens and hundreds places.
– The second period consists of thousands and ten thousands places.
– The third period consists of lakhs and ten lakhs places.

– The fourth period consists of crores and ten crores places.
• International System of Numeration: In the International system of numeration, we use ones,
thousands, millions and billions as periods.

– The first period consists of ones, tens and hundreds places.
– The second period consists of thousands, ten thousands, and hundred thousands places.

– The third period consists of millions, ten millions, and hundred millions places.
– The fourth period consists of billions, ten billions, and hundred billions places.
• Comparing large numbers: We have the following rules for comparing large numbers.

(i) The more the number of digits, the greater is the number.
(ii) If two numbers have the same number of digits, the number with the bigger digit in the
leftmost place is greater.

(iii) If the left most digits are the same, we compare the next digit to the right and keep doing this
until the digits are different.

• Whole numbers include the natural numbers and 0.

• Representation of whole numbers on the number line: A number line is a pictorial representation of
numbers on a horizontal straight line.

0 1 2 3 4 5 6 7 8 9 10
Whole numbers on a number line are evenly placed.

• Supercells: In a table, supercells are the cells that have a number greater than all their neighbouring cells.

• Palindromes: Palindromes are numbers that read the same from left to right and right to left.
• Kaprekar Constant: The magical number ‘6174’ is known as the Kaprekar constant. We always reach

this number by applying the Kaprekar procedure to any four-digit number not having all digits identical.
• Estimation: Estimation is the process of finding an estimate or approximation that is usable for some
purpose. Estimation is done by rounding off to the nearest tens, or hundreds, or thousands. Estimation

can also be done using some logical methods also.
• There are several problems about numbers that seems very easy to pose, but very difficult to solve.
Indeed, numerous such problems are still unsolved (e.g., Collatz’s Conjecture).

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