Large Numbers: Arithmetic Operations and Solved Examples

Large numbers are the numbers much bigger than what we use in daily life.

• In the number system, the number that is bigger than the other numbers is called a large number.
• Examples of big numbers, that we do not use in daily life include 1 lakh, 1 million,1 billion, and so on.
• These large numbers are usually written in standard form for better readability.
• The population of the country or the amount in a bank account is represented by the positive large numbers.

Key Terms: Large numbers, Addition, Subtraction, Multiplication. Division, Positive numbers, Place value system, One billion, One million

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What are the Large Numbers?

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“The numbers much bigger than the numbers we generally use in daily life are called large numbers.”

We all learn to count numbers from single digits up to several digits using the place value system. This system is of two types

• Indian place value system
• International place value system

Indian Place Value System

In this system, large numbers written in standard form are grouped by commas, with each group called a period. These periods have specific names based on their position:

• Ones period: Rightmost group (last 3 digits)
• Thousands period: Next group to the left (2 digits)
• Lakhs period: Next group to the left (2 digits)
• Crores period: Next group to the left (2 digits), and so on.

International Place Value System

In this system, large numbers written in standard form are also grouped by commas, with each group called a period.

• Each period represents 3 digits.
• Periods are named as ones, thousands, millions, billions, and so on.

The below points show how to read and write very large numbers

• 1,000,000,000 are “one billion”.
• 1,000,000,000,000 are “one thousand billion”.
• 1,000,000,000,000,000 are “one million billion”.
• 1,000,000,000,000,000,000 are “one billion billion”.
• 1,000,000,000,000,000,000,000 are “a thousand billion billion” and so on…

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Addition of Large Numbers

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The column addition method is used for adding large numbers.

• Step 1: Write the numbers vertically, one below the other, aligning the digits by their place value.
• Step 2: Start from the rightmost column (ones place) and add the digits in that column.
• Step 3: If the sum in a column is greater than or equal to 10, carry over the tens digit to the next column (left side) and add it to the digits in that column.
• Step 4: Repeat steps 2 and 3 for each subsequent column (tens, hundreds, thousands, etc.) moving leftward.

Addition of Large Numbers Example

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Subtraction of Large Numbers

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Subtracting large numbers can be done using a method called column subtraction. The process involves the following steps:

• Step 1: Write the numbers vertically, one below the other, aligning the digits by their place value.
• Step 2: Start from the rightmost column (ones place) and subtract the digits in that column.
• Step 3: If the top digit is smaller, borrow 1 from the digit above (tens, hundreds, etc.) in the top number.
• Step 4: After borrowing subtract the digits in the current column.
• Step 5: Repeat steps 2-5 for each subsequent column (tens, hundreds, thousands, etc.) moving leftward.

Subtraction of Large Numbers Example

Read Also: Arithmetic progressions practice material

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Multiplication of Large Numbers

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The following are the steps for multiplying large numbers

• Step 1: Write the numbers vertically, one above the other.
• Step 2: Start from the rightmost digit in the bottom number.
• Step 3: Multiply this digit by each digit in the top number.
• Step 4: Write down the product of each multiplication below the line, and shift one place to the left according to the digit's place value in the top number.
• Step 5: Repeat steps 2-4 for each digit in the bottom number, moving leftward.
• Step 6: Finally, add all the individual products you wrote down.

Multiplication of Large Numbers Example

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Division of Large Numbers

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Large numbers are divided using the long division method, which is applicable to all division problems.

• There is a dividend, which is divided by the divisor to produce a result known as the quotient, and sometimes a remainder.
• Division involves the complete cycle of division, subtraction, and multiplication.

Division of Large Numbers Example

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Things to Remember

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• Large numbers are the numbers much larger than the ones we use in daily life.
• For better readability, these large numbers are usually written in standard form.
• Examples of large numbers include 1 lakh, 1 million, and 1 billion.
• Large numbers are divided using the long division method.
• These are added using the column addition method.
• These are subtracted using the column subtraction method.