Introduction To Bhartiya System of Numeration

A comprehensive guide to the Bhartiya (Indian) System of Numeration, covering place value, periods, and large number representation for CBSE Class 11 Applied Mathematics.

The Structure of Bhartiya Numeration System

The Bhartiya System of Numeration, also known as the Indian Place Value System, is primarily based on grouping digits into periods of ones, thousands, lakhs, and crores. Unlike the International system, which groups digits in sets of three, the Indian system uses three digits for the first period (hundreds) and thereafter groups of two digits each.

Periods: [Crores] [Lakhs] [Thousands] [Ones] -> (XX, XX, XX, XXX)
Example 1: Represent the number 54321768 using the Indian place value system format.
Show Step-by-Step Solution

• Start from the rightmost digit and group the first three digits as the ones period: 768.
• Group the next two digits as the thousands period: 32.
• Group the next two digits as the lakhs period: 43.
• The remaining digits form the crores period: 5.

Answer: 5,43,21,768

Place Value and Face Value

In the Indian system, the place value of a digit is determined by its position in the sequence, while the face value remains the actual digit itself. For a number like 8,76,54,321, the place values are Ones (1), Tens (20), Hundreds (300), Thousands (4,000), Ten Thousands (50,000), Lakhs (6,00,000), Ten Lakhs (70,00,000), and Crores (8,00,00,000).

Place Value = Digit × Position Value (e.g., 5 in 50,000 is 5 × 10,000)
Example 1: Find the place value of the digit 9 in the number 92,45,678.
Show Step-by-Step Solution

• Identify the position of 9: Units, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs.
• The digit 9 is in the Ten Lakhs place.
• Multiply 9 by 10,00,000.

Answer: 90,00,000

Reading and Writing Large Numbers

Reading large numbers in the Indian system involves articulating the value within each period, followed by the name of the period. We move from left to right, combining the digits in each period (e.g., 'Forty-three lakh').

Read as: (Period Name of Crores) crore, (Period Name of Lakhs) lakh, (Period Name of Thousands) thousand, (Ones period)
Example 1: Write the number 2,05,06,008 in words.
Show Step-by-Step Solution

• Break down into periods: 2 (Crores), 05 (Lakhs), 06 (Thousands), 008 (Ones).
• Express each period: Two Crore, Five Lakh, Six Thousand, Eight.

Answer: Two crore five lakh six thousand eight