## Introduction to Numbers up to 10-Digits

There is a number so large that for you to count from 1 to that number, it would take years together. If you constructed a cube with a volume equal to that number, the cube would have to be more than 80 feet tall. The number we are talking about here is a Billion, and it is the smallest ten digit number, written as 1000000000. Just to give you a perspective about how large this number is, consider that your school is 3 miles from your house. You must have read about the planets in school and must have heard of Pluto. Well, the distance of the sun from Pluto is 3 billion miles. You take half an hour to reach your school from your house. So you would take a billion times more to reach the sun from Pluto.

## The Big Idea: Numbers up to 10-Digits

### A simple idea: The Importance of a Comma

As we said above, the smallest ten digit number is called a billion, and it is written by writing 1 followed by 9 zeroes. But just the different placement of the comma in two different number systems gives this number two different names.

The Indian system of numbers follows the 3:2:2 system of placing commas, so the smallest 10 digit number would be written as 100,00,00,000. Since the third comma after the 7th digit from right denotes the start of a crore, so this number would be called 100 crores in the Indian number system.

Let us now look at the 3:3 system of comma placement in the International number system. This number would be written as 1,000,000,000. Since the third comma after the 9th digit from right denotes the start of a billion, so this number would be called 1 billion in the International number system.

### How To Decompose 10 – digit numbers

Any ten digit number has place values up to 100 crores (or one billion). These are the names of the place values (starting from the right) in a ten-digit number:

- Digit 1 – Units
- Digit 2 – Tens
- Digit 3 – Hundreds
- Digit 4 – Thousands
- Digit 5 – Ten Thousands
- Digit 6 – Lakhs
- Digit 7 – Ten Lakhs / Millions
- Digit 8 – Crores / Ten Millions
- Digit 9 – Ten Crores / Hundred Million
- Digit 10 – Hundred Crores / Billion

So let us take a random ten digit number - 5338652930, and see how it gets decomposed.

Digit 1 Place Value = 0 x 1 = 0

Digit 2 Place Value = 3 x 10 = 30

Digit 3 Place Value = 9 x 100 = 900

Digit 4 Place Value = 2 x 1000 = 2000

Digit 5 Place Value = 5 x 10000 = 50000

Digit 6 Place Value = 6 x 100000 = 600000

Digit 7 Place Value = 8 x 1000000 = 8000000

Digit 8 Place Value = 3 x 10000000 = 30000000

Digit 9 Place Value = 3 x 100000000 = 300000000

Digit 10 Place Value = 5 x 1000000000 = 5000000000

## How is it important?

### A 10 Digit Number We All Should Be Familiar With

The population of the world would soon be 8 billion. To get an idea of how large that number is, digest the fact that even with so many companies making so many people so rich, at present there are only 140 people out of this 8 billion who are worth more than $7 billion. If this number was not big enough, just remember that the population of the world was a 5 billion in 1987, and in the next twelve years it became 6 billion, and in another 12 years it crossed 7 billion.

The following facts will give you an idea of how large a number 7 billion is:

- If all the 7 people in the 2011 population had an average height of 5 feet (considering children as well), and were laid end to end, they would cover the distance to the moon 27 times and would go \({1 \over 14}\) of the way to the sun.
- An ant weight next to nothing, but if you were to weight 7 billion ants together, they would together tip the scales at 23 tonnes!
- If someone walked along the earth's equator and took 7 billion steps, the diameter would be covered 106 times!!

That is how big the smallest 10 digit number is.