Introduction to Large Numbers
Large numbers are those numbers that have a bigger value than the numbers that we use in daily life. Such numbers tend to create a sense of fear among children and they often skip solving problems that have large numbers in them. For example, 1 million, 1 billion, etc., are large numbers that are used either to show the population of a country or express large amounts of money in a bank account.
|1.||Meaning of Large Numbers|
|2.||Addition of Large Numbers|
|3.||Subtraction of Large Numbers|
|4.||Multiplication of Large Numbers|
|5.||Division of Large Numbers|
|8.||FAQs on Large Numbers|
Meaning of Large Numbers
Everyone learns how to count numbers at a very young age starting from a single-digit up to seven digits. This is done with the help of the place value system. There are two place value systems that are followed - the Indian Place Value System and International Place Value System.
While writing large numbers, we always keep the place value system in mind to ensure that it is written correctly. According to the Indian place-value system, when a number is written in the standard form, each group of digits separated by a comma is called a period. These periods are named as ones, thousands, lakhs and so on. The ones period consists of the first three digits of the large number, starting from the right. The thousands period consists of the next two digits. The lakhs period consists of the next two digits and it continues.
According to the International place value system also, the numbers are divided into periods. These periods are named as ones, thousands, millions, billions and so on. In this system, each period has three digits.
Let us look at this example: 12,457, 891. According to the International Place Value system, this is read as twelve million, four hundred fifty-seven thousand, eight hundred ninety-one.
Some other large numbers are read and written as follows:
1,000,000,000 = one billion
1,000,000,000,000 = one thousand billion
The following table shows how to read and write numbers as per the International Place Value System.
Addition of Large Numbers
We add large numbers in the same way as we work with other numbers. We arrange the numbers in a column according to their place values. The addition process begins from the ones column, the next tens column, the hundreds column, and so on. The numbers that need to be carried forward, are placed in the adjacent column along with the existing numbers. This entire process has to be followed until the last column where we get our final number.
Example 1: Find the sum of the following large numbers: 67,34,903, 2,61,89,403, and 12,79,40,674.
First, we arrange the numbers in columns according to their place value and then we add them.
Therefore, the sum of the given numbers is 160,864,980.
Subtraction of Large Numbers
For subtraction of large numbers, the same order of columns that were used for addition is followed. Once the numbers are arranged in the columns, we begin with ones and move forward to the left side. Numbers are borrowed as and when required from the left side.
Example 2: Find the difference between the following large numbers: 67,89,540 and 23,78,954.
First, we arrange the numbers in columns according to their place value and then we subtract them.
Therefore, the difference of the given numbers is 4,410,586.
Multiplication of Large Numbers
The multiplication of large numbers is done in the same way as the other numbers. After the numbers are placed in the columns, we take the bottom number and start with the number in ones place. We multiply this number with all the numbers in the top row and write the product below the line. In the next step, before we start multiplying the next number, we need to hold the tens place by placing a zero in the ones place, so, we write zero in ones place. Then, we repeat the process and take the next number from the bottom number and multiply it with all the numbers in the top row. Place the product in the same line where we had placed the zero. Once we get the product of both the numbers, we add them column-wise to get the final answer.
Example 3: Multiply the large number 74,597 by 32.
Therefore, the product of the given numbers is 2,387,104.
Division of Large Numbers
Division of large numbers is done by the long division method which is similar to all division problems. There is a dividend, which is divided by the divisor, to give a result called the quotient and sometimes a remainder. The process of division includes the complete cycle of division, subtraction, and multiplication.
Example 4: Divide the large number 1,260,257 by 37.
Example 1: Find the sum of these two large numbers: 234,679 and 4,659,129.
Solution: Adding the two large numbers by applying the method mentioned above.
234,679 + 4,659,129 = 4,893,808
Therefore, the sum of the numbers is 4,893,808.
Example 2: Multiply the large number 135,012 by 12.
Solution: Multiplying the large number by applying the method mentioned above.
135,012 × 12 = 1,620,144
Therefore, after multiplication, we get 1,620,144 as the product.
FAQs on Large Numbers
What is the Meaning of Large Numbers?
Large numbers are usually bigger numbers that are not used so much in our day-to-day lives. They are mostly used while calculating a country's population or while counting the money in a bank account. For example, 1 million and 1 billion are considered as large numbers.
How do we Read Large Numbers?
While reading or writing large numbers, we always begin from the left and move on to the right. It is always better to position the numbers according to their place value system. According to the Indian place-value system while reading large numbers we divide the numbers into periods named as units, thousands, and lakhs. For example: 24,12,340 is written and read as twenty-four lakh, twelve thousand, three hundred and forty. According to the International place value system, the periods are named as ones, thousands, millions, and billions, and so on. So, the same number 2,412,340 is written and read as two million, four hundred twelve thousand, three hundred and forty.
What is 1000000 in Large Numbers?
1,000,000 is read as one million as per the international place value system.
Is a 10-digit Number a Billion?
Yes, a 10-digit number is read as a billion. For example, 4,000,000,000 is read as Four billion.
How do we Write Large Numbers?
Large numbers are written in their expanded form keeping in mind their respective place values. For example, 456790 is written as four lakh, fifty-six thousand, seven hundred and ninety as per the Indian place value system. As per the International place value system, the same number is written as four hundred fifty-six thousand, seven hundred and ninety.