 # Knowing our Numbers Class 6 Maths Chapter 1 Notes

## CBSE Class 6 Maths Notes Chapter 1 Knowing Our Numbers

With the help of numbers, one can count concrete objects. They help us find which collection of objects is bigger and accordingly arrange things in increasing or decreasing order. Knowing our Numbers Class 6 Maths Chapter 1 Notes

It is easy to count a large number of objects these days. Also, we can communicate large numbers with the help of suitable names for numbers.

## CBSE Class 6 Maths Notes Chapter 1 Knowing Our Numbers

### Ex : 1.1 –  Introduction

• We can count concrete objects with the help of numbers.
• They help us know which collection of objects is bigger and accordingly arrange things in increasing or decreasing order.
• We know addition, subtraction, multiplication and division.
• We have observed patterns in number sequences.
• A number is a mathematical value used to count and measure different objects.
• With the help of the numbers, we all can add, subtract, divide and multiple.

### Ex : 1.2 –  Comparing Numbers

Comparing numbers when the total number of digits is different :

• The number with the most number of digits in the largest number by the magnitude
• The number with the least number of digits is the smallest.
• Example: Consider numbers: 24, 133, 7, 445, 2005.
• The largest number is 2005 (4 digits) and the smallest number is 7 (only 1 digit).

### Ex : 1.2.1 –  How Many Numbers Can You Make

• While forming numbers from the given digits, we should check carefully whether the condition under which the numbers are to be formed is satisfied or not.
• The given condition must essentially be satisfied.
• Thus, to form the largest number from the given four digits 7,9,3,2 without repeating a single digit, we must be careful to use all the given four digits.
• As such, the largest number can have 9 only as of the leftmost digit.

Comparing numbers when the total number of digits is same

• The number with the highest leftmost digit is the largest number.
• If this digit also happens to be the same, we look at the next leftmost digit and so on.
• Example: 240, 385, 456, 395, 570.
• The largest number is 570 (leftmost digit is 5) and the smallest number is 240 (on comparing 240 with 385, 4 is less than 8).

Ascending order and Descending order:

• Ascending Order: Arranging numbers from the smallest to the greatest.
• Descending Order: Arranging numbers from the greatest to the smallest number.
• Example: Consider a group of numbers: 32, 12, 90, 433, 9999 and 109020.
They can be arranged in descending order as 109020, 9999, 433, 90, 32 and 12, and in ascending order as 12, 32, 90, 433, 9999 and 109020.

### Ex : 1.2.2 –  Shifting Digits

• Changing the position of digits in a number changes the magnitude of the number.
• Example: Consider a number 678. If we swap the hundredths place digit with the digit at units place, we will get 876 which is greater than 678.
• Similarly, if we exchange the tenth place with the units place, we get 687 which is greater than 678.

### Ex : 1.2.3 –  Introducing to 10,000

• The smallest 2-digit number is 10 (ten).
• The largest 2-digit number is 99.
• The smallest 3-digit number is 100 (one hundred).
• The largest 3-digit number is 999.
• The smallest 4-digit number is 1000 (one thousand).
• The largest 4-digit number is 9999.
• The smallest 5-digit number is 10,000 (ten thousand).
• The largest 5-digit number is 99999.
• The smallest 6-digit number is 1,00,000 (one lakh).
• The largest 6-digit number is 9,99,999.
• This carries on for higher digit numbers in a similar pattern.

### Ex : 1.2.4 –  Revisiting Place Value

• The place value1 of a digit at one place is the same as the digit.
• The place value of a digit at tens place is obtained by multiplying the digit by 10.
• Similarly, the place value of a digit at hundreds place, thousands place, ten thousand places,… is obtained by multiplying the digit by 100, 1000, 10000, …, respectively.

### Ex : 1.2.5 –  Introducing to 1,00,000

• The greatest five-digit number is 99,999.
• If we add 1 to this number, we get 1,00,000 which is the smallest six-digit number.
• It is named as one lakh. It comes next to 99,999.
• Also, 10 × 10,000 = 1,00,000.

### Ex : 1.2.6 –  Larger Numbers

• The greatest six-digit number is 9.99.999.
• Adding 1 to it, we get 10,00,000 which is the smallest seven-digit number. It is called the ten lakh.
• The greatest seven-digit number is 99.99,999. Adding 1 to it, we get 1.00.00.000 which is the smallest eight-digit number. It is called one crore.
• 1 hundred = 10 tens
• 1 thousand = 10 hundred = 100 tens
• 1 lakh = 100 thousand = 1000 hundred
• 1 crore = 100 lakhs = 10,000 thousand

### Ex : 1.2.7 –  An aid in reading and writing large numbers

• The first comma comes after hundreds of places, the second comma comes after ten thousand places and the third comma comes after ten lakh places and marks a crore. Shagufta’s indicators help us to read and write large numbers. These are also useful in writing the expansions of the numbers.
• These are as follows:

T La La T Th Th H T O

• Commas also help us in reading and writing large numbers.
• In the Indian system of Numeration, we use ones, tens, hundreds, thousands and then lakhs and crores.
• Commas are used to mark thousands, lakhs and crores.

### Ex : 1.3 –  Large Numbers in Practice

Large numbers can be easily represented using the place value. It goes in the ascending order as shown below:

### Ex : 1.3.1 –  Estimation

There are several situations in which we do not need the exact quantity but need only an estimate of this quantity. Estimation means approximating a quantity to the desired accuracy.

### Ex : 1.3.2 –  Estimating to the nearest tens by rounding off

• The estimation is done by rounding off the numbers to the nearest tens. Thus, 17 is estimated as 20 to the nearest tens; 12 is estimated as 10 to the nearest tens.
• Estimating depends on the degree of accuracy required and how quickly the estimate is needed.

### Ex : 1.3.3 – Estimating to the nearest hundreds by rounding off

• Numbers 1 to 49 are closer to 0 than to 100. So they are rounded off to 0.
• Numbers 51 to 99 are closer to 100 than to 0, and so are rounded off to 100.
• Number 50 is equidistant from 0 and 100 both. It is customary to round it off as 100.

### Ex : 1.3.4 – Estimating to the nearest thousands by rounding off

• Numbers 1 to 499 are nearer to 0 than 1000, so these numbers are rounded off like 0.
• The numbers 501 to 999 are nearer to 1000 than 0, so they are rounded off as 1000.
• Number 500 is customarily rounded off as 1000.

Example:

### Ex : 1.3.5 – Estimating outcomes of number situations

• There are no fixed rules for the estimation of the outcomes of numbers.
• The procedure depends on the degree of accuracy required.
• It is important to know is how quickly the estimate is required?

### Ex : 1.3.6 – To estimate sum or difference

• We round off the given numbers and then find their sum or difference.
• Estimations are used in adding and subtracting numbers.
• Example of estimation in addition: Estimate 7890 + 437.
Here 7890 > 437.
Therefore, round off to hundreds.
7890 is rounded off to       7900
437 is rounded off to      +   400
Estimated Sum =              8300
Actual Sum       =              8327
• Example of estimation in subtraction: Estimate 5678 – 1090.
Here 5678 > 1090.
Therefore, round off to thousands.
5678 is rounded off to       6000
1090 is rounded off to    – 1000
Estimated Difference =     5000
Actual Difference       =     4588

### Ex : 1.3.7 – To estimate products

• We round off the numbers to their greatest places and then carry out the multiplication or division.

### Ex : 1.4 – Using Brackets

When we need to carry out more than one first turn everything inside the brackets into a single operation, we use brackets to avoid confusion. We number and then do the operation outside.

BODMAS

While solving mathematical expressions, parts inside a bracket are always done first, followed by of, then division, and so on.

• Example :

[(5 + 1) × 2] ÷ (2 × 3) + 2 – 2 = ?

[(5 + 1) × 2] ÷ (2 × 2) + 2 – 2….{Solve everything which is inside the brackets}

= [6 × 2] ÷ 6 + 2 – 2…..{Multiplication inside brackets}

= 12 ÷ 6 + 2 – 2……{Division}

= 2 + 2 – 2……{Addition}

= 4 – 2…….{Subtraction}

= 2

### Ex : 1.4.1 – Expanding Brackets

We expand brackets systematically maintaining a track of steps.

Using brackets

1. Using brackets can simplify mathematical calculations.
2. Example :
3. 7 × 109 = 7 × (100 + 9) = 7 × 100 + 7 × 9 = 700 + 63 = 763
4. 7 × 100 + 6 × 100 = 100 × (7 + 6) = 100 × 13 = 1300

### Ex : 1.5 – Roman Numerals

• Digits 09 in Roman are represented as : I, II, III, IV, V, VI, VII, VIII, IX, X
• Some other Roman numbers are : I = 1, V = 5 , X = 10 , L = 50 , C = 100 , D = 500 , M = 1000

Rules for writing Roman numerals

• If a symbol is repeated, its value is added as many times as it occurs.
Example: XX = 10 + 10 = 20
• A symbol is not repeated more than three times. But the symbols X, L and D are never repeated.
• If a symbol of a smaller value is written to the right of a symbol of greater value, its value gets added to the value of the greater symbol.
Example: VII = 5 + 2 = 7
• If a symbol of a smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.
Example: IX = 10 – 1 = 9.
• Some examples: 105 = CV, 73 = LXXIII and 192 = 100 + 90 + 2 = C  XC  II = CXCII

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