## Introduction to Numbers up to 8-Digits

Let us start with an interesting anecdote. Almost 3 centuries ago, when modern society first started to count numbers, the count was done by a system of tallying. So 4 straight marks were followed by a fifth one placed across the four made a count of five. Such sets of 5 were used to count up to 10, then 50, 100, 1000 and more. In England, there were actually wooden tally sticks made for the purpose of counting larger numbers. These tally sticks were stored in the House of Commons. They were finally abolished in 1826 and were ordered to be burnt. But the burning took place inside the House, and by mistake the furnishings caught fire. As a result, the House burnt down completely. This was depicted in a famous painting by Turner in 1835.

Imagine the number of tally sticks that would have been needed to count larger numbers like lakhs and millions. Today we go up one more level in our journey towards large numbers, and we will talk about 8 digit numbers today.

## The Big Idea: Numbers up to 8-Digits

### A simple idea: The Introduction of a crore

As we moved from 6 digits to 7 digits, we got acquainted with a new word – million. This word is used in the international numbering system and is equivalent to 10 lakhs, where a lakh is a word used in the Indian numbering system and is equal to a hundred thousand.

When we move on to 8 digits, we get another new word, but this time in the Indian system of numbering. The smallest 8 digit number is 1 followed by 7 zeroes and is written as 10000000. If we write this number in both ways, this is how they would look:

Indian Number System – 100,00,000

International Number System – 10,000,000

As per the international system, the placement of the commas can easily tell you that the number is 10 million because the comma after the sixth digit from right signifies 1 million. In the Indian system, you will see that there is 100 on the left of the comma following the first 5 digits from the right. So this number is 100 lakhs. We have a word for 100 lakhs, and it is called a crore. So as per the Indian numbering system the smallest 8 digit number is a crore, which is equal to a hundred lakhs, or ten million.

### The two ways of looking at 8 – digit numbers

Eight digit numbers can be expressed in both the Indian systems of numbers and the International system of numbers. Let us take the random eight digit number 24864701. Let us look at the two ways we can write this number:

Indian: 2,48,64,701 (this can be read as two crores forty-eight lakhs sixty-four thousand seven hundred and one)

### International: 24,864,701 (this can be written as twenty-four million, eight hundred sixty-four thousand seven hundred and one)

How To Decompose 8 – digit numbers

Any eight digit number has place values up to one crore (or ten million). These are the names of the place values (starting from the right) in an eight 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

So let us take the seven digit number we discussed above - 24864701, and see how it gets decomposed.

Digit 1 Place Value = 1 x 1 = 1

Digit 2 Place Value = 0 x 10 = 00

Digit 3 Place Value = 7 x 100 = 700

Digit 4 Place Value = 4 x 1000 = 4000

Digit 5 Place Value = 6 x 10000 = 60000

Digit 6 Place Value = 8 x 100000 = 800000

Digit 7 Place Value = 4 x 1000000 = 4000000

Digit 8 Place Value = 2 x 10000000 = 20000000

## How is it important?

### Zeroes in 8 – digit numbers

There are 8 place values in every 8 digit number, and any number from 0 to 9 can be put into any of these place values. There is only one exception. If the leftmost place value ( Ten Millions / Crores) is zero, then it becomes a 7-digit number. If the digits in 24864701 are rearranged to place the zero on the extreme left, the number becomes 04864721, in which case it becomes the 7-digit number 4864721.