# CBSE Class 6 Maths Revision Notes Chapter 1

## CBSE Class 6 Mathematics Chapter 1 Revision Notes – Knowing Our Numbers

A number is the basic unit of mathematics through which various calculations are performed. Without numbers, mathematics would not have existed. So, it is crucial for learners to be well-versed in numbers to develop an understanding of mathematics.

Class 6 Mathematics Chapter 1 Notes introduce students to the world of numbers. This chapter is very important as they learn new concepts like estimation, the use of commas, shifting digits, etc., which are fundamentals of mathematics. A strong foundation will help students understand advanced concepts in higher classes. Therefore, Extramarks has prepared comprehensive notes on the chapter “Knowing Our Numbers” to help students gain conceptual clarity.

At Extramarks, subject matter experts prepare these notes with the updated pattern of questions, trends, and the syllabus of the CBSE board. These notes are comprehensive yet concise. Students can refer to these notes to understand the concept better and give their best performance in the exam hall. Therefore, they can access quality notes that follow the latest syllabus and guidelines of CBSE from the Extramarks website.

## Revision Notes For CBSE Class 6 Mathematics Chapter 1

### Knowing Our Numbers Class 6 Mathematics Chapter 1 Notes

Numbers are the elementary components of mathematics. To perform numerical calculations, students must have all the necessary conceptual clarity about numbers themselves. Extramarks offers extensive revision notes to introduce students to numbers. The Class 6 Mathematics Chapter 1 Notes cover the following topics:

• Comparing Numbers
• Shifting Digits
• Introducing 10,000
• Revisiting Place Value
• Introducing 1,00,000
• Larger Numbers
• Use of Commas
• Estimation
• To Estimate Sum or Difference
• To Estimate Products
• Using Brackets
• Roman Numerals
• FAQs

All these topics are discussed extensively to remove all doubts and give conceptual clarity to students.

### Class 6 Mathematics Chapter 1 Notes

Class 6 Mathematics Chapter 1 Notes provided by Extramarks are well-structured and to the point. All the concepts are discussed step-by-step so that students can understand the logic behind every concept. They will be able to revise the entire chapter quickly and utilise more time for practice before the exam.

### Comparing Numbers

• Numbers are compared to find out whether they are greater than, less than, or equal to other numbers.
• When two numbers are given, the number with more digits is considered the greater number. Between 23 and 3, the former is the greater number.
• If the number of digits is the same in both numbers, then the leftmost digits are to be checked. The number with the greater leftmost digit is the greater one. 826 is greater than 625.

### Shifting Digits

• When a certain number is given, it is possible to make new numbers by simply interchanging the positions of its digits.
• It is important to meet the requirements and criteria while forming new numbers. A digit cannot be repeated within the same number.
• Thus, the largest number that can be formed with the four digits 4, 6, 3, and 9 is 9643, with 9 as the leftmost number.
• If the digits shift their places, new numbers will be formed.
• The number 6394 is smaller than the original number.

### Introducing 10,000

• The greatest two-digit number is 99.
• Similarly, 999 and 9999 are the greatest three-digit and four-digit numbers respectively.
• It is observed that the smallest three-digit number, 100 (hundred), comes right after the greatest two-digit number, 99.
• The smallest number with four digits is 1000 (one thousand) which comes after the greatest three-digit number 999 (nine hundred and ninety-nine).
• Similarly, the smallest number containing five digits is 10,000 (ten thousand) which comes after the greatest four-digit number, 9999 (nine thousand nine hundred and ninety-nine).

### Revisiting Place Value

• Every digit in a given number has a certain value based on its position. This value is called the place value of the digit.
• For example, the place value of 8 in the number 84 is 8 x 10 = 80 because 8 is in the tens place.
• The place value of 3 in the number 5347 is 3 x 100 = 300 as 3 possesses the hundreds place.
• The place value of 5 in the same number is 5 x 1000 = 5000 because 5 occupies the position of thousands places.

### Introducing 1,00,000

• 1,00,000 (one lakh) is the smallest six-digit number.
• It has been already observed that the lowest five-digit number comes right after the greatest four-digit number.
• Similarly, the smallest six-digit number 1,00,000 comes after the greatest five digit-number 99,999 (ninety-nine thousand nine hundred and ninety-nine).
• 1 is added to the largest five-digit number to produce the smallest six-digit number.

### Larger Numbers

• Larger numbers are those numbers which are greater than the numbers used in daily life.
• When the number of students in a class is counted, usually two-digit numbers are required.
• If the number of total students in a school is to be counted, three-digit or four-digit numbers are sufficient.
• But if the total number of students from ten different schools in the area is counted, the number can go up to four or five digits.
• The concept of larger numbers is necessary to understand when and where to use them.

### Use of Commas

• Commas are used to read and write large numbers easily.
• Further, commas make it easy to distinguish between the Indian Number System and the International Number System.
• In the Indian Number System, the first comma is put after three digits starting from the right end; and after that, commas appear after every two digits from the right.
• Thousand, lakh, and crore are marked by using commas after three, five, and seven digits respectively.
• The International Number System follows a different rule. Here, commas are placed after every three digits from the right.
• The International Number System denotes thousands and millions by inserting commas after three and six numbers.

### Estimation

• Estimation is the process of acquiring an approximate value when only a rough idea of a number is required instead of the exact figure.
• Estimation helps avoid unnecessarily complicated calculations. In a certain cricket match, if 1,013 people come to see the match, it is easy to take 1,000 as the estimate of total spectators for conveying the number of people present in the gallery.
• An estimated number is obtained by rounding off the exact number to a number close to it.

### To Estimate Sum or Difference

• Estimation is applied in the operations of large numbers.
• If two large numbers are to be added, they can be rounded off for the convenience of calculation.
• For example, 11,075 and 7,009 are the numbers to be added. The estimated values of these numbers are 11,000 and 7,000. Their sum of 18,000 is closer to the sum of the original numbers, ie., 18,084.
• Approximate numbers can be taken in a similar way while calculating the difference between two numbers. Consider 999 and 515 as the given numbers. Round the numbers up to 1,000 and 500 to make the calculation easy. The difference is 500 which is near the difference between the original numbers, i.e., 484.

### To Estimate Products

• Round off the given numbers to the numbers closer to them.
• Closer numbers should be chosen in a way that could be multiplied easily.
• For multiplying 99 by 12 take the approximate values 100 and 10. Now, the calculation becomes easy. The estimated product is 1,000.

### Using Brackets

• When multiple operations are to be performed on given numbers, brackets are used to avoid erroneous results.
• If the numbers are given in the following way 12 x 5 + 3, it is difficult to understand whether the multiplication should be done first or the addition.
• In this situation, brackets play an important role.
• When the expression is written like (12 x 5) + 3, complete the multiplication first according to the BODMAS rule. Then add the other number to the product.
• So, 63 will be the right answer.

### Roman Numerals

• The numbers used in daily life belong to the Hindu-Arabic number system. Roman numerals are another way of representing the same numbers.
• For example, 1 is written as I; 2 is written as II. 3, 4, 5, 6, 7, 8, 9, 10, etc., are denoted by III, IV, V, VI, VII, VIII, IX, and X respectively.

### Conclusion

Class 6 Mathematics Chapter 1 Notes will help students revise and memorise all of these concepts more effectively. As these notes cover all the concepts, students need not search for any other study material. The notes are prepared as per the CBSE curriculum, and hence, are beneficial for quick revisions before exams. What’s more? Class 6 Mathematics Chapter 1 Notes provided by Extramarks are easily accessible from the website.

### 1. Why is the concept of comparing numbers important?

Comparing numbers is an important concept in the number system. Numbers must be compared to find out which number is greater or which one is smaller to arrange them in increasing or decreasing order.

### 2. What is the estimation of numbers in mathematics?

Estimation or approximation is a method of rounding off a number to obtain a closer number. This method is especially helpful when dealing with large numbers as it simplifies complicated calculations. Besides, estimation is also used when an idea of a number is needed instead of the exact figure.

### 3. What is the chapter Knowing Our Numbers all about, according to the Class 6 Mathematics Chapter 1 Notes?

Numbers are the rudimentary units that form the very basis of mathematics. This chapter explains the various mathematical operations performed on numbers like addition, subtraction, multiplication, and subtraction. When the calculations become complicated, the methods of estimation and placing brackets are of great help. New numbers can also be formed by shifting the digits of a given number.

There are two popular systems of writing numbers, such as the Hindu-Arabic numerical system and the Roman numerical system. The Hindu-Arabic system is used in mathematics, whereas the Roman system can be found on the dials of watches and clocks, page numbers of books, schedules for classes, etc.

### 4. What are the basic concepts of numbers that one should understand at the initial stage?

Students of Class 6 should become familiar with the various concepts of numbers. The CBSE board curriculum introduces students to concepts like comparison of numbers, shifting digits, estimation of sum, difference and products, usage of commas in a number, significance of brackets in calculations, the two methods of writing numbers, and so on. All of these concepts are essential for the students of class 6 for understanding complicated concepts at a later stage.

Extramarks has carefully designed the notes to help the students understand all of these concepts.

### 5. What is meant by “shifting digits” according to the Class 6 Mathematics Chapter 1 Notes?

Shifting digits is a simple method of making new numbers from an existing number by exchanging the positions of its digits. The new numbers can be greater than or less than or equal to the original number. Refer to the Class 6 Mathematics Chapter 1 Notes for further clarification on the topic.

### 6. Explain in brief the difference between ascending order and descending order.

Both ascending and descending orders use the concept of comparison of numbers. But the difference is, in ascending order, numbers are arranged from the smallest to the greatest, and in descending order, numbers are placed in reverse order.