Question

What is the value of 1 billion in crores?

Answer 1

Hint: Try to write one billion following the international numeral system and one crore following Indian numeral system. Then find the ratio of the two to express one billion into crores.

Complete step-by-step answer:

A numeral system is a writing system for representing numbers. It is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
Mostly the decimal number system is followed all around the world as a standard numeral system.
There are two numeral systems that can be fined in the decimal numeral system on the basis of name assigned to the place value.
These are: -
International numeral system:
In the international numeral system, the place value of the digit is assigned as ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, hundred million, billion, ten billion, hundred billion and so on starting from the leftmost digit in the number. Three digits are grouped together with a comma separating them in this numeral system.

Indian numeral system:
In the Indian numeral system, the place value of the digit is assigned as ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, ten crores and so on starting from the leftmost digit in the number. First three digits are grouped together and then in pairs of two are grouped with a comma separating them in this numeral system.

We need to find the value of 1 billion in crores.
First, we need to find the numerical representation of billions.
By following the international numeral system, one billion is written as,
$1,000,000,000$
As the number of digits in a billion = 10
In exponential power of ten, one billion $={10}^9$
Similarly, by following the Indian numeral system, one crore can be written as,
$1,00,00,000$
As the number of digits in a crore = 8
In exponential power of ten, one billion $={10}^7$
Hence taking the ratio of the two values, we get
$$\begin{gathered} {\displaystyle \frac{\text{One Billion}}{\text{One Crore}}}={\displaystyle \frac{{10}^9}{{10}^7}}={10}^{9-7}={10}^2 \\ \text{One Billion}=100\times \text{One Crore}=100\text{ Crores} \end{gathered}$$

Hence the value of 1 billion in crores is equal to 100 crores.

Note: Commas are placed in the numeral systems to simplify the readability of the numbers and also in this way they can be written easily. The position of comma is essential in distinguishing between the Indian and the international numeral system. After ten crores in Indian system, one can represent the numbers as hundred crores, thousand crores and so on.