CBSE Class 6 Maths Notes Chapter 1 Knowing Our Numbers
In this page we have covered CBSE Class 6 Maths Notes Chapter 1 Knowing Our Numbers. Let us explore the fascinating world of numbers and their various properties. Understanding numbers is fundamental to mastering mathematics, and this chapter lays the groundwork for your journey into more advanced mathematical concepts. Let’s dive into the basics of numbers, their classifications, and the different ways we can manipulate and understand them.
Introduction to Numbers
Understanding Numbers
- Numbers are essential arithmetic values used to represent magnitudes.
- They help quantify and compare different quantities and entities around us.
Comparing Numbers
Different Number of Digits:
- A number with more digits is larger in magnitude. Example: Among 45, 678, 3, 8901, 56789, the largest is 56789 (5 digits) and the smallest is 3 (1 digit).
Same Number of Digits:
- Compare numbers starting from the leftmost digit. If the digits are equal, continue comparing the next digits.
- Example: Among 451, 459, 672, 345, 349, the largest is 672 (leftmost digit 6), and the smallest is 345 (compare 345 and 349, 4 is less than 9).
Ordering Numbers
Ascending Order
- Arranging numbers from smallest to largest.
Example: 10, 25, 67, 234, 789, 1234.
Descending Order
- Arranging numbers from largest to smallest.
Example: 1234, 789, 234, 67, 25, 10.
Forming Numbers with Given Digits:
- Different numbers can be formed by rearranging given digits.
Example: Using digits 2, 5, 7, 1:
– Largest number: 7521
– Smallest number : 1257 (0 cannot be the leftmost digit).
Shifting Digits
- Changing the position of digits alters the number’s magnitude.
Example: Changing 576 to 765 increases its value. Swapping the tens and units place in 576 gives 756, which is greater than 576.
Place Value
- Each place in a number is worth ten times the place to its right.
Example: In the number 576:
– Place value of 5 = 500
– Place value of 7 = 70
– Place value of 6 = 6
Larger Numbers and Estimates
Large Numbers
- Large numbers are represented using place values, increasing in powers of ten.
Example:
– 8 digits: 10,000,000 (1 crore)
– 7 digits: 1,000,000 (10 lakhs)
– 6 digits: 100,000 (1 lakh)
– Largest 3-digit number + 1 = Smallest 4-digit number.
– Example: 999 + 1 = 1000.
| 8th Digits | 7th Digits | 6th Digits | 5th Digits | 4th Digits | 3rd Digits |
|---|---|---|---|---|---|
|
100 Million
(1 crore) |
1 Million(10 Lakhs) |
Hundred Thousands(1 lakh) |
Ten Thousands |
Thousands
|
Hundreds |
Estimation
- Approximating a number to the nearest plausible value.
Example:
-75843 to the nearest tens: 75840
– 75843 to the nearest hundreds: 75800
– 75843 to the nearest thousands: 76000
– 75843 to the nearest ten thousands: 80000
Estimating Sum or Difference
- Used for quick approximations in addition and subtraction.
-Example: Estimate 6872 + 432.
– Round 6872 to 6900 and 432 to 400.
– Estimated Sum = 7300 (Actual Sum = 7304).
Estimating Products
- Round off factors to their highest place value before multiplying.
-Example: Estimate 198 x 34.
– Round 198 to 200 and 34 to 30.
– Estimated Product = 200 x 30 = 6000 (Actual Product = 198 x 34 = 6732).
BODMAS Rule
- Order of operations: Brackets, Orders (i.e., powers and roots), Division and Multiplication, Addition and Subtraction.
-Example: [(4 + 2) × 3] ÷ (3 × 2) + 3 – 1.
Step 1. Solve inside brackets first: [6 × 3] ÷ 6 + 3 – 1.
Step 2. Multiplication: 18 ÷ 6 + 3 – 1.
Step 3. Division: 3 + 3 – 1.
Step 4- Addition and Subtraction: 6 – 1 = 5.
Roman Numerals
- Roman numeral system uses letters I, V, X, L, C, D, M.
- Rules:
1. Repeated symbols are added: XX = 20.
2. Symbols are not repeated more than three times.
3. Smaller symbols before larger ones are subtracted: IX = 9.
4. Smaller symbols after larger ones are added: VI = 6.
Example:
1. 100 = C
2. 58 = LVIII
3. 149 = CXLIX
Frequently Asked Questions on CBSE Class 6 Maths Notes Chapter 1 Knowing Our Numbers
Q1. What is the full form of BODMAS?
Ans: Brackets of Division Multiplication Addition and Subtraction.
Q2. What are Roman Numbers?
Ans: Roman numbers are a symbolic representation of the numbers.