Why Are Large Numbers Important in Maths?
What are the Large Numbers?
Large numbers can produce a sigh of fear amongst the children. Before solving the question, only the children are scared. They might even feel like skipping the problem and moving forward. These big numbers are quite prevalent. The numbers which seem to be quite more significant than used in the daily chores of life could technically be included within the definitions of large numbers. Even adults who would have undergone the chapter of the number system in their childhood would also have faced issues and the fear of large numbers.
Meaning of Large Numbers
We have clearly understood what children fear at times. Now it is a tad bit easier to see the scenario and tackle the problem which is generated. The sole reason which causes the problem is the unaccustomed born of these large numbers with which the child may not seem to be habituated.
Let us make you aware of these numbers in simple formats. We all must have heard of counting numbers up till seven digits or maybe fewer digits. We know that the numbers are divided into different bunches like ones, tens, and hundreds, which come under the category of ones, then we have a thousand and ten thousand, later we have lakhs and ten lakhs and lastly crores and ten crores. The above-given information comes under the Indian place value chart. If we consider it in the international place value system then till ten thousand it will be the same but after that comes a hundred thousand, one million ten million, a hundred million, billion and so on. In the Indian system from the right after the first period of three digits, all other periods consist of two digits; however, in the international system, each period consists of three digits.
Before reading a number, we divide the numbers into periods starting from the right. The first period which consists of three digits, is called the unit period. The second period which consists of two digits, is called the thousands period. The third period is called the lakhs period, and it consists of two digits. The last period is called the crores period. It consists of two digits in case of a nine-digit number.
Let me explain by providing some examples, 23456789 is a number, in Indian style, we will write as two crores thirty-four lakhs fifty-six thousand seven hundred eight nine. Whereas in the international style, if a number is 2323202, then we will write as two million three hundred twenty-three thousand two hundred two.
Addition of Large Numbers
We follow a simple procedure; firstly, we arrange the numbers in columns and then add the digits in each column, starting with one's. If any numbers need to be carried, then carry it over to the next column and combine it with the digits in that particular column. This process is to be followed until the last column.
Example - Add 71,24,567;83,45,67,890 and 12,45,07,687.
First, arrange the given numbers in columns and then add them up.
71 24 567
+ 83 45 67 890
+ 12 45 07 687
----------------------------------
96 62 00 144
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Subtraction of Large Numbers
We follow simple steps; firstly, we arrange the numbers column-wise. Then we start construction again, starting with ones. Lastly, we borrow wherever we find the necessity, keeping in mind from the left side of the place.
Example - Subtract 48,32,46,132 from 98,24,64,372.
First, arrange the number column-wise then subtract them.
98 24 64 372
- 48 32 46 132
---------------------------
49 92 18 240
---------------------------
Multiplication of large numbers
The process is simple and similar, like we do the multiplication of two or three-digit numbers.
Example - Multiply 8231 by 2345
8235
× 2345
-----------------
41155 ( 8231× 5)
329240 ( 8231× 40)
2469300 ( 8231× 300)
1646200 ( 8231× 2000)
----------------
19301695
------------------
Division of Large Numbers
The division process is also the same, just as we do normal division.
Example - Divide 628936 by 48.
Step 1 - Since the division has two digits, take the first two digits from the left. 48 goes once in 62. Write 1 in the quotient and 48 below 62.
Step 2 - 62- 48= 14. Bring down 8. 48 goes in 148 three times. Write 3 in quotient's place and subtract 144 from 148. 148-144= 4.
Step 3 - Bring down next digit 9. 48 goes once in 49. Write 1 in the quotient's place, and we get 49-48=1.
Step 4 - Bring down 3. We get 13. 48 does not go with 13. Put 0 in quotient's place and bring down 6. We get 136.
Step 5 - 48×2= 96. 136-96=40.
The quotient is 2; the remainder is 40.
FAQs on Large Numbers: Meaning, Examples & Place Value Explained
1. What are large numbers in mathematics, and can you give some examples?
In mathematics, large numbers are numbers that are significantly bigger than what we typically use for simple counting. They usually have many digits, like 6, 7, 8, or more. These numbers help us describe vast quantities. For example, the population of a large city might be 50,00,000 (fifty lakh), and the distance from the Earth to the Sun is about 15,00,00,000 kilometres (fifteen crore kilometres).
2. What is the main difference between the Indian and International systems of numeration?
The primary difference lies in how digits are grouped using commas and the names given to these groups. In the Indian system, we group the last three digits first, followed by groups of two (e.g., 5,09,87,123). In the International system, we group digits in threes from the right (e.g., 50,987,123). This changes the names we use:
1,00,000 (one lakh) in the Indian system is 100,000 (one hundred thousand) in the International system.
1,00,00,000 (one crore) in the Indian system is 10,000,000 (ten million) in the International system.
3. How do we form the greatest and smallest possible numbers using the digits 7, 1, 0, 5, and 9?
To form the greatest and smallest numbers from a given set of digits, you need to arrange them based on place value.
To form the greatest number, you arrange the digits in descending order (from largest to smallest). Using 7, 1, 0, 5, 9, the greatest number is 97,510.
To form the smallest number, you arrange the digits in ascending order (from smallest to largest). However, you cannot place '0' at the beginning. So, you place the next smallest digit first, followed by 0. Using 7, 1, 0, 5, 9, the smallest number is 10,579.
4. Why is 'estimation' an important skill when working with large numbers?
Estimation, or rounding off, is a crucial skill because it simplifies complex calculations and makes large numbers easier to understand. It helps in quickly checking if an answer is reasonable without needing an exact calculation. For example, if you are shopping and your items cost ₹1,980, ₹5,120, and ₹2,950, you can estimate the total as ₹2,000 + ₹5,000 + ₹3,000 = ₹10,000. This gives you a quick, practical idea of the total expense, which is a core concept for the CBSE 2025-26 syllabus.
5. Where can we see real-life examples of large numbers being used?
Large numbers are used all around us to measure and describe the world. Some common real-life examples include:
Government Budgets: National or state budgets are often discussed in terms of 'lakhs of crores'.
Scientific Data: The distance between stars, the number of cells in a human body, or the age of the Earth are all expressed using large numbers.
Finance: The total value of transactions in a country's stock market in a day.
Population Statistics: The population of countries like India (over 140 crore) or the world (over 8 billion).
6. How does comparing large numbers help in practical situations?
Comparing large numbers is a fundamental skill for making informed decisions. For instance, a business owner might compare the annual revenue of two different years, like ₹5,45,67,890 and ₹5,67,89,123, to determine business growth. Similarly, when buying a house, you would compare the prices to find the better deal. The process involves checking the number of digits first; the number with more digits is larger. If the digits are the same, you compare them from the leftmost place value to the right.
7. Is there such a thing as the 'largest number' in mathematics?
No, there is no 'largest number'. This is because numbers are infinite. For any large number you can think of, no matter how many digits it has, you can always create a larger one simply by adding 1 to it. For example, if you consider 99,99,99,999 (ninety-nine crore ninety-nine lakh ninety-nine thousand nine hundred and ninety-nine) to be a large number, adding 1 gives you 1,00,00,00,000 (one hundred crore), which is even larger.
