Hello, and welcome to your mathematics lesson. Today, we explore numbers in Indian and International Systems. By the end of this lesson, you will understand how to read and write large numbers using two different systems, and you will see how these systems compare with each other.
Let us start with some basic definitions. A numeral is simply a symbol that represents a number. Numeration, on the other hand, is the way we express that number in words. For example, the numeral 3 is written as the word "three." The numeral 15 becomes "fifteen," and 72 becomes "seventy two."
There are two main systems of numeration used around the world. The first is the Indian system, also known as the Hindu-Arabic system. The second is the International system. Let us explore each one carefully.
The Hindu-Arabic or Indian system of numeration is the decimal system used worldwide. It was developed by ancient Hindu mathematicians in India and later carried to the West by Arab scholars. This system uses ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each symbol is called a digit.
Among these digits, 0, 2, 4, 6, and 8 are even numerals, while 1, 3, 5, 7, and 9 are odd numerals.
To read large numbers easily, the Indian system groups digits into periods. Starting from the right and moving left, we have four periods. The first three digits form the ones period: ones, tens, and hundreds. The next two digits form the thousands period: thousands and ten thousands. The next two digits form the lakhs period: lakhs and ten lakhs. The final two digits form the crores period: crores and ten crores.
When reading a number, we read all digits in the same period together, followed by the period name. We do not say the word "ones" for the ones period. Commas are used to separate these periods in the numeral form.
Let us see some examples. The number 7456123 is written with commas as 74,56,123 and read as "seventy four lakh fifty six thousand one hundred twenty three."
The number 225437 becomes 2,25,437 and is read as "two lakh twenty five thousand four hundred thirty seven."
For a larger number like 61786425, we write 6,17,86,425 and say "six crore seventeen lakh eighty six thousand four hundred twenty five."
Here are three important rules to remember when using the Indian system.
First, never use plural forms for periods. Write 5493 as "five thousand four hundred ninety three," not "five thousands four hundreds."
Second, do not use the word "and" before tens and ones. Say "five thousand four hundred ninety three," not "five thousand four hundred and ninety three."
Third, do not put commas when writing the number in words. Commas belong only in the numeral form.
Now let us turn to the International system of numeration. This system is widely used in Western countries and in scientific contexts. Like the Indian system, it also groups digits into periods, but the grouping is different.
Starting from the right, the first three digits form the ones period: ones, tens, and hundreds. The next three digits form the thousands period: thousands, ten thousands, and hundred thousands. The next three digits form the millions period: millions, ten millions, and hundred millions. Beyond that, we have the billions period.
Notice the key difference: in the International system, each period after the ones contains three digits, not two.
Let us read the same numbers using this system. The number 7456123 becomes 7,456,123 and is read as "seven million four hundred fifty six thousand one hundred twenty three."
The number 225437 is written 225,437 and read as "two hundred twenty five thousand four hundred thirty seven."
The number 61786425 becomes 61,786,425 and is read as "sixty one million seven hundred eighty six thousand four hundred twenty five."
Now comes an important question: how do these two systems relate to each other? Let us compare them directly.
One lakh in the Indian system equals one hundred thousand in the International system. Ten lakhs equal one million. One crore equals ten million. Ten crores equal one hundred million.
The placement of commas clearly shows which system is being used. In the Indian system, commas appear after every two digits from the right, except for the first three digits. In the International system, commas appear after every three digits from the right.
For example, take the number five crore eight lakh sixteen thousand four hundred seven. In the Indian system, we write this as 5,08,16,407. In the International system, the same number becomes 50,816,407 and is read as "fifty million eight hundred sixteen thousand four hundred seven."
Another example: thirty-two crore fifty lakh eight thousand six hundred. In Indian form: 32,50,08,600. In International form: 325,008,600, read as "three hundred twenty five million eight thousand six hundred."
Let us work through two complete examples to solidify your understanding.
Example one: using the Hindu-Arabic system, read the number 850746. We place this in our period columns: eight in the lakhs place, five in the ten thousands, zero in the thousands, seven in the hundreds, four in the tens, and six in the ones. With commas: 8,50,746. Reading: "eight lakh fifty thousand seven hundred forty six."
Example two: write "forty one million five hundred fifty thousand five hundred twenty seven" in numeral form using the International system. Forty one million gives us 41 in the millions period. Five hundred fifty thousand gives us 550 in the thousands period. Five hundred twenty seven gives us 527 in the ones period. The answer is 41,550,527.
Let us recap the key points from today's lesson.
First, the Indian or Hindu-Arabic system uses periods of ones, thousands, lakhs, and crores, with two digits in each period after the first.
Second, the International system uses periods of ones, thousands, millions, and billions, with three digits in each period after the first.
Third, commas are placed differently: after the first three digits from the right, then after every two digits in the Indian system, and after every three digits in the International system.
Fourth, one lakh equals one hundred thousand, and one crore equals ten million.
Fifth, when writing numbers in words, never use plural forms, never use "and" before tens and ones, and never use commas.
Sixth, always identify which system is being used by looking at the comma placement before reading or writing any large number.
That brings us to the end of this lesson on Numbers in Indian and International Systems. Practice converting numbers between these two systems, and soon you will read and write large numbers with confidence. Keep exploring, keep learning, and I look forward to our next mathematics lesson together.