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 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.
• 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
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).
• 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 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').
• 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