Knowing our numbers- An overview
Knowing our Numbers is the first chapter in NCERT for the 6th class. It is very important to go through this chapter thoroughly as it would create a foundation for students for the further chapters in the book. The topics that are discussed in this chapter are listed below-
Introduction
Comparing Numbers
Large Numbers in practice
Estimation
Using brackets
Roman Numerals
Introduction
The first section is the introduction which introduces the importance of numbers that help us to count or arrange the objects and are used in many different contexts. These are arithmetic values that help us to convey the magnitude of all the objects that are present around us.
Comparing Numbers
In order to understand mathematical concepts such as greater than or equal to, the comparison of numbers is important. The subtopics of comparing numbers are:
How many numbers can you make?
In this part, students will learn how they can make numbers from given digits. Numbers will be formed in such a way that no digit is repeated in a single number and there cannot be two exact numbers. Students will also learn about the different orders of numbers which are ascending (smallest to greatest) and descending (greatest to smallest).
Shifting digits
In this part, students will learn how a small shift in the digits of the numbers can make a difference in the value of the number.
Introducing 10,000
In this part, students learn about the greatest 3-digit number which is 999, and what happens when we add a 1 to 999.
Revisiting place value
In this part, students will learn about the expansion of 2-digit, 3-digit, and 4-digit numbers and the place value for each digit.
Introducing 1,00,000
In this part, students will learn about the greatest 5-digit number which is 99999, and what happens when 1 is added to 99999.
Larger Numbers
In this section, students will learn about the greatest and smallest 6-digit, 7-digit, and 8-digit numbers which include numbers like 10 lakh and one crore.
An aid in reading and writing large numbers
This section will explain to the students how to read and write large numbers by identifying the digits in one place, tens place, hundreds place, and so on.
Use of commas
This chapter will also help the students to learn the use and importance of commas in the number system.
Large Numbers in practice
Students will learn about large numbers and how they can be written in shorter forms by using units such as centimeters and meters, grams and kilograms, meters and kilometers, etc.
Estimation
This section will help the students to learn about the approximate or near values of certain numbers. Let us have a look at the subsections.
Estimating the nearest tens by rounding off
In this section, students will learn how to round off numbers to the nearest tens. Suppose 13 is a number that lies between 10 and 20, but since it is closer to 10, therefore it would be rounded off to the nearest tens which are 10.
Estimating the nearest hundreds by rounding off
Here students will learn how to round off numbers to the nearest hundreds, for example, 310 lies between 300 and 400 but are closer to 300, therefore it will be rounded off to 300.
Estimating the nearest thousands by rounding off
Just like nearest tens and hundreds, students will also learn about how to round off numbers to the nearest thousand. For example, 8600 is a number that lies between 8000 and 9000 but since it is closer to 9000, it would be rounded off to the nearest thousand which is 9000.
Estimating outcomes of number situations
Students will learn about the situations where we need to answer quickly for how to add numbers quickly by keeping the digits of the numbers being added in the same place and rounding them off to the nearest values.
To estimate sum or difference
It is not always necessary that you need to round off, therefore in this section students will learn why and when we need to round off.
To estimate products
Here the students will learn about the general rule which states that estimating while multiplying can be done by rounding off each factor to its greatest place and then multiplying those factors.
Using brackets
Students will learn about the use of brackets and how they are used in order to avoid confusion while doing mathematical calculations. In expanding brackets the students will learn the systematic procedure for the removal of brackets.
Roman Numerals
Students will study one of the earliest systems which are roman numerals and are still used in many places
FAQs on Knowing our Numbers
1. What is estimation in mathematics? How to round off numbers?
Estimation in mathematics is making an assumption or rounding off a particular number for better understanding and quick calculation. For instance, 25,158 people have attended a recent football match. However, for better reference, this number is rounded-off to its nearest round number, i.e. either 25,000 or 25,500.
On the other hand, referring 25,128 as 26,000 is not a correct estimation. Additionally, to round off numbers using this method, you can take help of the estimation and use the nearest estimated number. You can use this estimation method to perform mathematical operations as well. Moreover, this method helps in quick calculation and representing an exact figure that is often difficult to calculate.
2. Which is the lowest five-digit number?
10, 000 is the smallest five-digit number. Moreover, it appears by adding 1 with the highest four-digit number, i.e. 9,999. The pattern followed for this calculation is, 9+1=10=10X1; 99+1=100=100X1; 999+1=1000=1000X1; 9,999+1=10,000=10,000X1.
Furthermore, you can use this method to calculate an even larger number with six, seven-digits. This process further explains that, highest single-digit number + 1 = smallest two-digit number; greatest two-digit number + 1 = smallest three-digit number; highest three-digit number + 1 = smallest four-digit number, and so on.
3. What is the International System of Numeration?
Similar to the Indian system of numeration, there is an International system of numeration. However, unlike the Indian system, here commas mark thousands and millions. One million is equal to a thousand thousands.
Moreover, in this system, commas come after every three-digit from the right. Here the first one marks thousand and the next one is for millions. For instance, 45,520,598 is read as forty-five million five hundred twenty thousand five hundred and ninety-eight according to the international system. On the other hand, in the Indian system, it will be read as four crores fifty-five lakhs twenty thousand five hundred and ninety-eight.
Additionally, in the international system, billion is used to denote any number larger than millions. Thus, 1 billion = 1000 million.
4. What is the purpose of a comma?
Commas play a pivotal role in writing, learning and remembering large numbers. The Indian System of Numeration uses ones, tens, thousands, lakhs and then crores. Commas help in marking these. Moreover, in the Indian system commas are used in indicating thousands, lakhs, and then crores.
Furthermore, the initial comma comes after hundreds place, i.e. three digits from the right. After that, the second comma comes after two digits, which marks lakh. Finally, the third comma comes after another two digits, i.e. seven digits from the right. Thus, it marks crore.
5. What are Some of the Importance of Estimation of Numbers?
Estimation is one of the most important skills that one possesses and it is not possible for the students to determine if the answer is correct or not if they lack these skills. Estimation of numbers is important as it helps to possibly determine the correct and reasonable answers. Estimations can make a calculation quicker, easier, and realistic if done properly.
6. What is the Reason behind studying Roman Numerals?
Roman numerals are a part of the numerical system that was studied in ancient Rome. The numerals include combinations of letters from Latin alphabets which are used to represent different values. Studying Roman numerals may help the students in understanding the ancient roman culture and think about numbers in different ways.
7. What are Some of the Uses of Brackets in Mathematics?
Brackets can be of various types such as parentheses, square and curly brackets. Using brackets helps to create groups and in order to gain more clarity about the order of the mathematical operations that are to be performed in an equation.
8. What is meant by the Place Value in the Number System?
The value that a digit represents on the basis of the position of the digit in a number is known as the place value of the digit. The place value can be tens, hundreds, thousands, and so on. For example, the place value of 9 in 2998 is hundreds and it represents the hundredth place. To learn more about the place value in detail, students can visit Vedantu.
9. What is meant by BODMAS?
BODMAS is an abbreviation for a bracket, orders, division, multiplication, addition, and subtraction. It is one of the most important rules in mathematics which is followed to do calculations in maths. It is according to this rule the sequence is followed while performing mathematical operations.