### Theory:

A system of numeration is a system for expressing numbers with the help of digits in a consistent manner.

There are two types of number system:

- Indian numeral system (Hindu-Arabic number system)
- International numeral system

What is the Indian numeral system?

This system was invented between the \(1st\) and \(3rd\) centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the \(9th\) century, and then it came to known as the Hindu-Arabic system. The system later spread to Europe. It is the most widely used system of numerals.

The place values of digits are

**Ones**,**Tens**,**Hundreds**,**Thousands**,**Ten Thousands**,**Lakhs**,**Ten Lakhs**,**Crores**, and so on.Example:

Consider the number 61,85,09,372 the place values of each digit are:

\(2\) – Ones

\(7\) – Tens

\(3\) – Hundreds

\(9\) – Thousands

\(0\) – Ten Thousands

\(5\) – Lakhs

\(8\) – Ten Lakhs

\(1\) – Crores

\(6\) – Ten Crores

\(7\) – Tens

\(3\) – Hundreds

\(9\) – Thousands

\(0\) – Ten Thousands

\(5\) – Lakhs

\(8\) – Ten Lakhs

\(1\) – Crores

\(6\) – Ten Crores

**Let us go through the Indian numeral system place value table**:

Periods on Ones:

Place value | Hundreds | Tens | Ones |

Number | \(100\) | \(10\) | \(1\) |

Number of zeros | \(2\) | \(1\) | \(0\) |

Periods on Thousands:

Place value | Ten Thousands | Thousands |

Number | \(10000\) | \(1000\) |

Number of zeros | \(4\) | \(3\) |

Periods on Lakhs:

Place value | Ten Lakhs | Lakhs |

Number | \(1000000\) | \(100000\) |

Number of zeros | \(6\) | \(5\) |

Periods on Crores:

Place value | Ten Crore | Crore |

Number | \(100000000\) | \(10000000\) |

Number of zeros | \(8\) | \(7\) |