Large Numbers for Class 5 [+12 Practice Worksheets]

This is a comprehensive lesson plan for teaching large numbers to grade 5 students. The lesson is designed to make the concepts easy and engage students with activities like quizzes, practice questions, worksheets, visual aids like images and videos, and real-life examples.

Teachers can use this guide as a reference for delivering the concepts to students and engaging them in the classroom with the various questions and examples given in this page.

For parents, there are 12 downloadable practice worksheets that they can use for their kids.

In this blog, you will learn:

• Numbers up to 7 digits

• Indian and International Systems of Numeration

• Face Value and Place Value

• Expanded Forms

• Comparing and Ordering Numbers

• Forming the Greatest and Smallest Numbers

• Roman Numerals

 

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What Are Large Numbers?

Large Numbers are quantities much greater than we usually experience in daily life. In fields like space science, math, and economics, large numbers help us see very big things. They describe the size of the universe or a country's wealth.

Examples of Large Numbers:

1. 1,000 (One Thousand): This is the first number with four digits and is commonly used for counting people or things.

2. 1,000,000 (One Million): This is often used to describe populous regions or vast amounts of money. For example, there are a million people living in a town.

3. 1,000,000,000 (One Billion): This number often appears with measures like a country's GDP or a company's tech worth.

4. 1,000,000,000,000 (One Trillion): This huge number can mean national debts or huge budgets.

5. 10⁶ (One Million in Scientific Notation): We use it to shorten large numbers. For example, 10⁶ means one million.

6. Googol (10¹⁰⁰): This number is even greater. It's so large that it's bigger than anyone needs in a day-to-day life. It's an imaginative approach to consider higher mathematics like quantum concepts.

 

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Numbers Up to 7 Digits

A large number is a number with more than three digits. Students must know how to handle values up to 7 digits. A range can have up to 7 digits, so it ranges from 1,000 to 9,999,999. For instance, 7 digits compose the variety 3,245,678. When the students get on to handling large numbers, they will be dealing with numbers as high as 10 million.

Example: 3,285,978 (This is a seven-digit number.)

In a 7-digit number, each digit has a specific place value. Here’s how it breaks down:

3,285,978

In the Indian System of Numeration - Thirty-two lakhs eighty-five thousand nine hundred and seventy-eight.

In the International System of Numeration - Three million two eighty-five thousand nine-hundred and seventy-eight.

Examples:

The population in a City: The population of Uttar Pradesh state is about 244,000,000.

Source: Wikipedia

National or State Budget: The GDP (Gross Domestic Product) of India for the year 2023 is Rs. 294.65 lakh crores or Rs. 2950,00,00,00,00,000.

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Indian and International Systems of Numeration

Knowing Indian Systems of Numeration is essential for large numbers. Both systems present numbers in cycles of three digits, but their names differ.

Indian System of Numeration

In the Indian System of Numeration, numbers are grouped into ones, thousands, lakhs, and crores. Every cluster includes either two or three digits with comma separation.

• 1,000 = One thousand

• 10,000 = Ten thousand

• 1,00,000 = One lakh

• 10,00,000 = Ten lakh

• 1,00,00,000 = One crore

 

International System of Numeration

The International System of Numeration groups numbers in periods of thousands. In this scheme, the right separates the commas after every three digits.

• One thousand = 1,000

• One million = one million

• One billion = 1,000,000,000 (1 observed by way of 9 zeros)

 

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Face Value and Place Value

Face Value

The face value of a digit means the digit itself. A digit's face value will not change, no matter where the digit is in a particular number.

Example:

Let us take the number 4,582.

• The face value of 4 is 4,

• The face value of 5 is 5,

• The face value of 8 is 8,

• The face value of 2 is 2.

 

Place Value

The most critical thing of this issue is area price, in which the numeral is defined and referenced by using its function price, which includes 1s, 10s, 100s, countless numbers and so forth. The location price of an unpaired digit can be computed with the aid of figuring out the position of the digit inside the wide variety and multiplying it by the price of that function.

Example:

Using the same number 4,582:

• The place cost of 4 is: (four thousand or four × 1,000) = four,000.

• The area value of five is: (5 hundred or 5 × 1oo) = 500.

• The area value of eight is: (8 tens or 8 × 10) = 80.

• The vicinity value of 2 is: (2 ones or 2 × 1) = 2.

 

Difference Between Face Value and Place Value

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Expanded Form of Numbers

The expanded form shows how to write numbers. It shows the value of each digit. It breaks down values by their position. So, each digit is easy to interpret.

How Does Expanded Form Work?

Each digit in a number has a fixed place (ones, tens, hundreds, thousands, etc.).

To get the expanded form of a number:

1. Break into the place values.

2. Write as a sum of these values.

Let’s take the number: 3982

• Break into digits:

• 3 is in the thousandth's area: 3 × 1000 = 3000

• 9 is in the hundredth's place: 9 × 100 = 900

• 8 is in the tenth's place: 8 × 10 = 80.

• 2 is in the hundredth's place: 2 × 1 = 2.

• Write that as a sum:

• 3982 = 9000 + 900 + 80 + 2.

Questions: Expand 8782, 89452

 

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Comparing and Ordering Numbers

What is Comparing Numbers?

• Comparing numbers means checking two or more numbers. We want to see which is bigger, smaller, or if they are equal.

• We use the following symbols to compare numbers:

• > (greater than)

• < (less than)

• = (equal to)

 

Steps to compare

Step 1: Count the number of digits.

• • The number with greater digits is larger than the wide variety with fewer digits.

  • For instance: 4234 is greater than 234 because 4234 has 4 digits and 234 has 3 digits.

Step 2: Compare by digits.

• • If each number has identical digits, evaluate them from left to right. Check the thousand's, hundred's, ten's, and unit's locations..

  • For instance: Compare 4,562 and 4,591.

    • Thousands place: 4 is the same for both.

    • Hundreds place: 5 is the same for both.

    • Tens place: Since 6 < 9, we conclude that 4,562 < 4,591

 

 

Examples of Comparison

• The comparison of 3,245 and 2,876:

  • Thousands place: 3 > 2.

• Count the number of digits: Both the numbers are 4 digits.

• We'll start comparing with 3 from the leftmost digit:

• Hence, 3,245 > 2,876.

• Comparing 6,432 and 6,432:

• Count the digits: Both have 4 digits.

• Compare the digits: All of them are the same.

• Thus, 6,432 = 6,432.

 

Ordering Numbers

Ordering numbers means to arrange them in sequential order:

• • Ascending: From smallest to largest.

  • Descending: From largest to smallest.

Steps to Order

Step 1: Compare all the numbers using rules for comparison.

Step 2: Arrange them according to the required order:

• • In ascending order from smallest to largest.

  • In descending order from largest to smallest.

Examples:

1. Ordering numbers 3145; 4875; 2341; 5012 in ascending order:

Compare and Order: 2341 < 3145 < 4875 < 5012.

2. Ordering numbers 7321; 8459; 6784; 9210 in descending order:

Compare and Order: 9210 > 8459 > 7321 > 6784.

 

A Quick Tip to Remember

• "Ascending", which in reality means to go up, is like climbing stairs.

• "Descending", however, means to go down, like sliding down a hill.

 

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Creating the Largest and Smallest Numbers

Steps to Create the Largest Number

1. Store each digit in descending order (larger to smaller).

2. Make numbers and form the largest number.

Example:

• Digits: 4, 7, 1, 9

• Descending into: 9, 7, 4, 1

• Insert together: 9741

Thus, the largest number is 9741.

 

Steps for the Smallest Number

1. Arrange digits in ascending order (smaller to bigger).

2. Make numbers starting from the first smallest digit, then the second smallest, and so on.

3. Insert digits together: Smallest number.

4. If the smallest digit is 0, enter it in the second position (after the first non-zero digit) to avoid leading zeros.

Example:

• Digits: 5, 3, 0, 2

• Arranged: 0, 2, 3, 5

• As 0 is not the first, it has to adjust to the second position: 2035

• The smallest number is 2035.

 

Exercise

Consider these digits: 6, 3, 8, 1
Write the largest and smallest number from these digits.
What will happen if we place 0 in the first?

 

Important Note about Using the Digit 0

• If 0 is there among digits, one should excel in making sure not to be the first digit in making the smallest number.

• For example:

• Digits: 0, 4, 2, and 9

• In ascending order, these are in arrangement of: 0, 2, 4, and 9

• Bringing it together was adjusted for the uppermost item of finding: 2049

 

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Roman Numerals

• Roman numerals are those that enjoyed widespread use in ancient Rome

• This means they never used numerals from 0 to 9 like we do; they instead use letters to represent numbers.

Basic Roman Numbers

Here are a few basic Roman numerals and their values.

 

Rules for Writing Roman Numbers

Repetitive Rule

• You can repeat a numeral a maximum of three times by adding its value. Examples:

• III = 1 + 1 + 1 = 3

• XX = 10 + 10 = 20

• Note: You cannot repeat V, L, and D.

Additive Rule

• If a small number comes after a large number, add those numbers.
  Examples:

• VI = 5 + 1 = 6

• XV = 10 + 5 = 15

Subtractive Rule

• If a small number comes before a large number, subtract the small number from the large number.
  Examples:

• IV = 5 - 1 = 4

• IX = 10 - 1 = 9

Not More Than One Subtraction: A larger numeral cannot have a smaller numeral subtracted from it. 

Examples:

• IX is correct; but, IIX is incorrect.

 

Adding Roman Numbers

• Adding numerals involves following the main idea of addition and subtraction.
  Examples:

• 12 is the same as X + II, which equals XII.

• 29 is the same as X + X + IX, which equals XXIX.

• 44 is the same as XL + IV, which equals XLIV.

• 99 is the same as XC + IX, which equals XCIX.

• 2024 is the same as MM + XX + IV, which equals MMXXIV.

Examples of Common Roman Numerals

• 1 = I

• 2 = II

• 3 = III

• 4 = IV

• 5 = V

• 6 = VI

• 7 = VII

• 8 = VIII

• 9 = IX

• 10 = X

• 50 = L

• 100 = C

• 500 = D

• 1,000 = M

 

Below is an image of roman numerals.

 

Practice Questions:

• Write 23 in Roman.

• Write 47 in Roman.

• Write 2023 in Roman.

• Write 88 in Roman.

 

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Operations with Large Numbers

The fundamental 4 operations with big numbers are: Addition, Subtraction, Multiplication, and Division. The following describes the manner of carrying out them stepwise:

Addition of Large Numbers

Steps:

• Write the numbers in a column. Align them by means of area value (i.E. 'ones' underneath 'ones', 'tens' beneath 'tens', and so on).

• Begin or start from the rightmost digit or 'one's place'.

• If a column's sum exceeds 9, carry over the extra digit to the next column.

• Write the result under the horizontal line.

Example: Add 456981 to 223456

 

Subtraction of Large Numbers

Steps:

• Align the numbers in column form according to their place values.

• Subtract starting from the rightmost digit.

• If the upper digit is smaller than the lower digit, borrow a one from the next column for the upper digit.

• Write the result under the horizontal line.

Example: Subtract 219376 from 870512

 

Multiplication of Large Numbers

Steps:

• Write the more quantity on top and the smaller quantity beneath it.

• Start with the rightmost digit. Multiply every digit of the lowest number by each digit of the highest number.

• Write each end result on a new row, transferring it one area to the left for each new digit.

• Add up all rows to arrive at the final answer.

Example: Multiply 791 by 56

 

Division of Large Numbers

Steps:

• Write the bigger digit inner and the divider outside the box.

• Divide the first or left part of the variety you need to divide by using the quantity you want to divide it by way of.

• Write out the quotient above the department field.

• Multiply the quotient by the divisor. Then, subtract the result from the current part of the dividend.

• Bring down the next digit from the dividend. Repeat the method until you use all the digits.

Example: Divide 2359 by 17

Quotient: 138, Remainder: 13

These are some of the major operations on large numbers.

 

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Fun Facts

• The First Big Number: The first massive wide variety with 4 digits is 1,000. People use it for counting huge organizations of humans, like at a concert.

• Names of Big Numbers: One trillion has 12 zeros. Even larger numbers, together with a quintillion or a googol (10¹⁰⁰), are typically utilized in arithmetic and technology to measure vast portions.

• Fun with Roman Numerals: Roman numerals don’t have a symbol for zero.

• Giant Numbers in Real Life: Earth has a population of over eight billion human beings—written as 8,000,000,000. The Sun is moving at a distance of approximately 147.31 million km from the Earth.

• The Spell of Scientific Notation: Scientists use big numbers like 6.022 x 10²³ (Avogadro's Number) to count molecules.

• Counting to a Million: If you counted simply one quantity according to 2nd, it might take you more than eleven days to remember one billion would take over 31 years.

• Largest Known Prime Number: The largest prime number discovered so far has 24,862,048 digits. It is a member of an elite group called the Mersenne Primes. 

• World Records: The longest number ever written down was a decimal expansion of pi (π) comprising more than 31 trillion digits.

• Did you know that Roman numerals are still used? Such as in:

  • Clock faces.

  • Book chapters.

  • Movie sequels (e.g. Rocky II, Rocky III).

  • Years on monuments or the credits of movies.

   

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Quiz

1. What is the largest 7-digit number?

A) 9,999,999

B) 1,000,000

C) 9,000,000

D) 8,765,432

 

2. In the Indian system of numeration, what comes after ten lakh?

A) Ten crore

B) One crore

C) One billion

D) One million

 

3. What is the face value of the digit 5 in the number 45,678?

A) 50

B) 5

C) 500

D) 5,000

 

4. Write 2,345,678 in expanded form. Which option is correct?

A) 2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8

B) 20,000 + 3,000 + 400 + 50 + 600 + 78

C) 2,000,000 + 300,000 + 45,600 + 70 + 8

D) 2,000,000 + 340,000 + 5,600 + 70 + 8

 

5. Arrange the numbers in ascending order: 45,789; 23,456; 89,123; 67,890.

A) 45,789; 23,456; 89,123; 67,890

B) 23,456; 45,789; 67,890; 89,123

C) 89,123; 67,890; 45,789; 23,456

D) 67,890; 23,456; 45,789; 89,123

 

6. What is the Roman numeral for 88?

A) LXXXVIII

B) LXXVIII

C) XCIII

D) XCIX

 

7. What is the smallest number you can make using the digits 5, 0, 8, and 3?

A) 5,083

B) 3,508

C) 0,358

D) 3,058

 

8. If you write 2 million in scientific notation, what will it be?

A) 2×10^5

B) 2×10^6

C) 2×10^7

D) 2×10^4

 

9. Compare the numbers using <, >, or =: 5,678,901 and 5,687,091.

A) 5,678,901 < 5,687,091

B) 5,678,901 > 5,687,091

C) 5,678,901 = 5,687,091

D) None of the above

 

10. What is the place value of 4 in the number 4,123,567?

A) 4,000,000

B) 40,000

C) 400,000

D) 4,000

 

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Orchids' Resources

Click the button to download the ebook on large numbers

 

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Things you have learned!

• Learned what large numbers are and how they are used in real life, like counting people or money.
• Understood how to break down numbers into place value, face value, and expanded form to see what each digit really means.
• Explored how numbers are written differently in Indian and International systems, like using lakh or million, and where to put commas.
• Figured out how to compare, order, and create numbers, including making the biggest or smallest numbers from a set of digits.
• Got familiar with using Roman numerals and practiced adding, subtracting, and multiplying big numbers easily.