Knowing Our Numbers - How Large Can Numbers Get?

One fine morning Mr. Gulati was reading a ‘News Paper’ and was enjoying his morning tea in his Lawn. All of a sudden his son Hitesh and daughter Anju interrupted him by saying:

Anju: Dad ! we are arguing with each other saying for the last 5 minutes to decide which of the following two numbers is larger and how these numbers can be read:

Hitesh presented the two cut outs:

r. Gulati expressed his ignorance and joined them to continue the discussion by posing another question:

Have you noticed that the two numbers quoted above, both comprise of all the ten digits of our number system?

Can we say that either of the two numbers is the largest of the counting numbers?

In case you are given a chance to join this interactive session of Mr. Gulati’s family, how will you react?

Oh! Look at Anju and see how she has reacted:

Anju: No, Dad, I do not agree with you. Let us see what we shall get by adding ‘1’ to the number 1234567890.

We have 1234567890 + 1 = 1234567891 and clearly 1234567891 is a successor of 1234567890 and so 1234567890 > 1234567891

Mr. Gulati immediately clapped for Anju and made them understand:

“There is no largest number! Numbers get larger and larger by adding 1to a number and getting its successor. This process of getting the successors never stop and we never stop getting larger and larger numbers.

The reason for that is: if you had a really big number, say:

987 654 321 000 000 000 000 000 000 000 000 000 000

then you could create an even bigger number by simply adding 1 to the monster above:

987 654 321 000 000 000 000 000 000 000 000 000 000 + 1

= 987 654 321 000 000 000 000 000 000 000 000 000 001

and then you could make a bigger number again:

987 654 321 000 000 000 000 000 000 000 000 000 001 + 1

=987 654 321 000 000 000 000 000 000 000 000 000 002

and again:

987 654 321 000 000 000 000 000 000 000 000 000 002 + 1

= 987 654 321 000 000 000 000 000 000 000 000 000 003

and so on...

So, you see? Numbers just keep getting bigger and there's no stopping them. There is no one out there who can tell you what the biggest number of all is, because if someone comes up with the "biggest" number, you can always make it bigger by just adding one.

Hitesh still expressed his anxiety to know that how we can read the large numbers like the ones quoted by dad.

Mrs. Gulati who was busy with her kitchen work also enjoyed their discussion and got tempted to answer Hithesh’s quarry and joined them in the lawn.

She uttered:

“Very Large numbers with all its digits can be a pain to write out or to pronounce. So, our ancestors have invented names for these numbers to make life simpler. Some of these names are already known to you. Just recall the place value table which you have already learned.

Both – Anju and Hitesh framed the following place value table

Ten Thousands (Th)	Thousands (Th)	Hundreds(H)	Tens(T)	Ones (O)
10000	1000	100	10	1

Mrs Gulati extended this table and reproduced the same as follows:

-------	Crores		Lakhs		Thousands		Units
-------	Ten Crores	Crores	Ten Lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
-------	100000000	100000000	1000000	100000	10000	1000	100	10	1

She further said, “Units, hundreds, thousands, lakhs and crores etc. are called the periods in Indo – Arabian system of writing numbers. First three places from the right of a number form the unit’s period. Next two places i.e. 4^th and 5^th places thousands period and so on.”

Incidentally one of the neighbor’s guests also reached their and interrupted “I believe that we may read large numbers by referring to the following place value chart:

Mr. Gulati took the ball in his court and said, “Yes, in the International numeration system, we use ones, tens, hundreds, thousands, millions and billions etc. In this system, commas are put after every three digits from the right. In other words, each period consists of three digits and the place value chart is:

-------	Billions	Millions			Thousands			Units
-----	-----	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
----	-----	100000000	10000000	1000000	10000	10000	1000	100	10	1

In order to conclude with the interactive session, Mr. Gulati expressed his gratitude for his family members and extended a special vote of thanks to the American Guest for making this morning session interesting and fruitful. He further asked Anju and Hitesh to write all the numbers which appeared during to day’s discussions in words, in figures in International as well as in Hindu Arabic Systems of numeration.

What about you? Would also like to do the assignment given by Mr. Gulati to his children?

For practice, work on the following assignment too:

Assignment 1.1

1. Next number in the sequence 24683, 35794, 46805, 57916, --------- is ------------.

2. Write the number obtained in question 1 above in

a. Figures in (i) Hindu Arabic system, separating different periods by using commas

(ii) International System, separating different periods by using commas

b. Words in (i) Hindu Arabic system (ii) International System

c. Expanded form in (i) Hindu Arabic system (ii) International System
3. First 20 odd natural numbers in the sequence of all 6 digit numbers are:

Recall: (i) Numbers not divisible by 2 are odd numbers and numbers divisible by 2 are

even numbers.

(ii) Numbers having 0 , 2 or a multiple of 2 in its unit’s place is divisible by 2.

4. What is the sum of the first 5 natural even numbers starting with 543210?

3. Find the 7^th number in the series 1, 30, 500, 7000 ____________

4. How many counting numbers are there between 567890 & 589543

5. A certain amount of money was shared by 3 people equally. Each of them spent Rs. 40000 and the sum of the remaining amount was equal to the initial share each had got. What was the initial sum of money each had?

6. Which of the following are prime numbers?

(a) 20019 (b) 115024 (c) 1275555 (d) none

Recall: (i) Counting Numbers other than 1which are not divisible by any number other than 1 and number it self are called prime numbers and numbers other than 1 which are divisible by at least one number other than 1 are called composite numbers.

(ii) Numbers having sum of the digits divisible by 3 are divisible by 3.

(iii) Numbers having 0, or 5 in its unit’s place are divisible by 5.

7). The sum of any seven consecutive numbers is divisible by

a) 2 b) 7 c) 3 d) 11

8. Number 500000 is divided into 2 parts such that their difference is 302550. Find the 2 parts.

9. There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. Find the first number.

10. The sum of two times one natural number and three times another natural number is less than 24. If the first natural number is less than or equal to eight, the highest value of the second natural number is:

(a) 5 (b) 6 (c) 7 (d) 8 (e) 9

Our lives are ruled by numbers which set our Destiny. Knowing these Numbers that influence and rule our lives, we can find Success and build Wealth.