Knowing Our Numbers Class 6 Notes CBSE Maths Chapter 1 (Free PDF Download)

• When two numbers are given, the one with more digits is larger. If the number of digits in two numbers is the same, the number with the bigger leftmost digit is the larger. If this digit is the same as the previous one, we move on to the next digit, and so on.

• When creating numbers from supplied digits, it's important to check to verify if the requirements for forming the numbers are met. Thus, we must employ all four digits to construct the largest four-digit number from 7,8,3,5 without repeating a single digit; the greatest number can only contain 8 as the leftmost digit.

• 1000 is the lowest four-digit number (one thousand). It comes after the three-digit number 999. Similarly, 10,000 is the lowest five-digit figure. It's a ten-digit number that comes after the greatest four-digit number, 9999. Furthermore, 100,000 is the lowest six-digit figure. It is one lakh and comes after 99,999, the highest five-digit figure. In a similar way, this is true for higher digit numbers.

• Using commas makes it easier to understand and write big figures. In the Indian numeration system, commas appear after the first three digits, starting on the right, and every two digits beyond that. Thousand, lakh, and crore are separated by commas after 3,5 and 7 digits, respectively. Starting from the right, commas are put after every three numbers in the International system of numeration. After three and six figures, commas separate thousand and million, respectively.

• In many aspects of daily life, large numbers are required. For example, to calculate the number of pupils at a school, the number of people in a hamlet or town, the amount of money spent or received in major transactions (buying and selling), and to measure vast distances, such as between cities in a country or around the world.

• Remember that a kilo represents 1000 times larger, a centi represents 100 times smaller, and a milli represents 1000 times smaller, thus 1 kilometre equals 1000 metres, 1 metre equals 100 centimetres or 1000 millimetres, and so on.

• There are a few instances where we don't require an exact quantity but simply a fair guess or estimate. For example, when mentioning the estimated number of people that watched a certain international hockey match, such as 51,000, we do not need to give the actual figure.

• Estimation is the process of estimating a quantity to the desired level of precision. So, depending on our needs, 4117 can be estimated to 4100 or 4000, i.e. to the closest hundred or thousand.

• We must estimate the result of number operations in a variety of scenarios. This is accomplished by rounding the numbers and obtaining a rapid, approximate response.

• Checking solutions by estimating the outcome of numerical operations is useful.

• We may prevent misunderstanding by using brackets in cases when we need to do more than one number operation.

• We utilise the Hindu-Arabic number system. The Roman numeral system is another way to write numbers.
  
  

Knowing Our Numbers Class 6 Notes

Class 6 Maths Chapter 1 Notes

Here let us look into some of the important concepts covered in Class 6 Chapter 1 Maths Notes:

• Introduction to Numbers

• Comparing Numbers

• Shifting digits

• Introducing 10,000

• Revisiting place value

• Introducing 1,00,000

• Larger numbers

• Reading and writing large numbers

• Use of commas

• Large Numbers in Practice

• Estimation

• Estimating to the nearest hundreds by rounding off

• Estimating to the nearest thousands by rounding off

• Estimating outcomes of number situations

• To estimate sum or difference

• To estimate products

• Using Brackets

• Expanding brackets

• Roman Numerals

Now let us revise each topic of Knowing our Numbers Class 6 Notes briefly.

Comparing Numbers

We compare numbers to check whether they are greater than, or less than or equal to.

Ex: When we compare 24 and 36, we can conclude that 36 is greater than 24 or 24 is less than 36.

Similarly, when we compare larger numbers such as 5005 and 5010, we can say the number 5010 is larger than the number 5005. This is because the hundreds place and thousands place numbers are the same as 5 and 0, but when we compare the tens and ones place number we can conclude that the number 5010 is greater than the number 5005.

Shifting Digits

Shifting digits means that exchanging the digits to different places to compare them.

Ex: Consider the number 787. Here if we exchange the digits to a different place like shifting the number 8 from tens place to one place we get a new number 778. If we compare the original number with the new number we can conclude that the original number 787 is greater than the new number 778.

Similarly, if we have a number 777. Here if we exchange the digits to different places we will still end up with the same number as all the digits are the same in this number.

Introducing 10,000

We know that there are 99 two-digit numbers from 1 to 99. After 99 we will have three-digit numbers till 999. After 999 we will start with four-digit numbers till 9999. Now if we add 1 to 9999 we will get a five-digit number called “Ten thousand (10000)”.

Revisiting Place Value

The place gives the value of each digit in a number.

Ex: Place value of the digit 7 in the number 75 is 7 × 10 = 70 as 7 is in the tens place.

Place value of digit 6 in the number 675 is 6 × 100 = 600 as 6 is in the hundreds place.

Place value of the digits 4 in the number 4675 is 4 × 1000 = 4000 as 4 is in the thousands place.

Introducing 1,00,000

We got to know that when we add 1 to the largest 4 digit number we will get 10,000. Similarly, when we add 1 to the largest 5 digit number we will get the smallest 6 digit number called one lakh (1,00,000).

Larger Numbers

Larger numbers are considerably larger than those we use commonly in our daily life.

Ex: When we are counting the number of students in the class which will be usually a 2 digit number. But when counting the numbers of students in the school it will either be a 3 digit or 4 digit number which is larger than the 2 digit number. Similarly, if we are counting a number of students from 10 different schools then this number will be very large, say a 5 digit number.

So understanding the larger number will allow students to apply them wherever necessary in a proper way.

Use of Commas

Using commas in the numbers will make it easy to read the large numbers. Also using commas we can differentiate between the Indian number system and the International number system.

Ex: When we write a large number 456783 without commas it will be difficult to read, but if we separate these digits with commas we can easily read. So writing the number with commas 4,56,783 which is read as four lakh fifty-six thousand seven hundred and eighty-three.

Commas can also be used to differentiate between the Indian number system and the International number system. Consider the same number 4,56,783 in the Indian system which has three commas but in the International number system the number is just separated by two commas 456,783 which is read as four thousand fifty-six and seven hundred and eighty-three.

Estimation

Estimation is done to find a value that is close enough to the original value. Estimation is just rounding off the number to the nearest whole number to make it easily readable.

When estimating, the general rule is to look at the digit to the right of the one we want to estimate.

Estimation of numbers is usually done when we are dealing with larger numbers.

Ex: When we are counting the number of students in the school, it will take a lot of time to find the headcount of each student. At this time we will give an estimated number of students. Say if the total number of students in the school is 1139, we can give the count as 1140 which is a rounded-off number and also easy to read.

To Estimate Sum or Difference

In this section of Class 6 Maths Chapter 1 Notes, we will find how to estimate the numbers when they are being added or subtracted.

Ex: When we are adding two large numbers say 8705 and 5611. We will estimate these two numbers to be 8700 and 5600 whose sum is 14300. So the sum of the numbers 8705 and 5611 will be closer to this estimated answer.

Similarly when we are subtracting two large numbers 8720 and 5645. Here we will estimate the numbers to 8700 and 5600. If we subtract these two numbers we get the difference as 3100 which is the estimated difference between 8720 and 5645.

To Estimate Products

Round the numbers to some similar numbers that we can easily multiply to estimate the multiplication result (product).

Ex: If we have to find the product of two numbers 485 and 92, we will round off the numbers like 500 and 100. So the estimated product is 50000.

Using Brackets

When we are doing multiple operations on the numbers we use brackets to avoid confusion and to read the numbers properly.

Ex: If we have to find the solution to the equation 24 + 45 × 10. It will be difficult to find the answer as we don’t know which operation we have to use first. Do we have to use addition first or multiplication? This is when the application of brackets will play a pivotal role in determining the answer. So now using brackets we can write the equation as (24 + 45) × 10. By using the BODMAS rule first we will operate the numbers inside the brackets, so we will perform the addition first and then we will multiply the numbers. So the answer will be 69 × 10 = 690.

Roman Numerals

Roman Numerals are represented by using the combinations of different letters from the Latin alphabet.

Ex: The roman numbers I, II, III, IV, V, VI, VII, VIII, IX, X denote the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 respectively from the Hindu-Arabic numeral system.

Conclusion

The Class 6 Chapter 1 Maths Notes will help students to revise all the basic and important concepts of Knowing our Numbers. As these revision notes are prepared according to the NCERT curriculum students can use these revision notes to prepare for their exams. The Class 6 Maths Notes Chapter 1 is available completely free on the Vedantu platform where students can download a PDF version of these revision notes to ace their exams.