Category : 6th Class
NUMBER SYSTEM
FUNDAMENTALS
0, 1, 2, 3,4,5,6,7,8,9
All the other numbers are written using 10 symbols.
Example: 2, 3, 4, 5 etc.
Example: 243, 67842, 546380, etc. are numerals.
\[\Rightarrow \] Let us see the chart of Indian system and understand about Indian system.
Periods 
Crores 
Lakhs 
Thousands 
Ones 

Places 
Ten Crores 100000000 
Crores 10000000 
Ten Lakhs 1000000 
Lakhs 100000 
Ten Thousands 10000 
Thousand 1000 
Hundreds 100 
Tens 10 
Units 1 
Example: 67842678 = Six Crore Seventy Eight Lakhs Forty Two Thousand Six Hundred Seventy Eight
\[\Rightarrow \] Let us see the chart of International system and understand about International system.
Periods 
Millions 
Thousands 
Ones 

Places 
Hundred Millions 100000000 
Ten Millions 10000000 
Millions 1000000 
Hundred Thousand 100000 
Ten Thousands 10000 
Thousand 1000 
Hundreds 100 
Tens 10 
Units 1 
Example: 1234567 = One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven.
A comma is inserted after each period in HinduArabic system as well as British system.
Example:
1. Six Crore Seventy Eight Lakhs Forty Two Thousand Six Hundred Seventy Eight.
6, 78, 42, 678
2. One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven.
1, 234, 567
Place value and Face value
Example: Eighty two thousand four hundred seventy two, that is 82472.
The face value of 2 is 2. Similarly the face value of 7 is 7 and 4, 2 and 8 are 4, 2 and 8 respectively.
PLACE VALUE:
2 has the place value \[2\times 1=2\] (ones place)
7 has the place value \[7\times 10=70\] (Tens place)
4 has the place value \[4\times 100=400\] (Hundreds place)
2 has the place value \[2\times 1000=2000\] (Thousands place)
8 has the place value \[8\times 10000=80000\] (Ten Thousands place)
Note: Place value of a digit = (face value) \[\times \] (value of place).
ROMAN NUMBER
\[\Rightarrow \] Roman symbols and their corresponding IndoArabic Numerals.
Roman numerals 
I 
V 
X 
L 
C 
D 
M 
IndoArabic Numerals 
1 
5 
10 
50 
100 
500 
1000 
Roman Numerals Fundamental Rules
Example: \[III=1+1+1=3\]
\[XXX=10+10+10=30\]
\[CC=100+100=200\]
\[III=1000+1000+1000=3000.\]
It may "be note that no numerals can be repeated more than 3 times. Repetition is allowed only for symbols I, X and C.
Estimation
Examples:
1. 54 = 50 (to the nearest tens)
2. 543 = 500 (to the nearest hundreds)
3. 5678 = 6000 (to the nearest thousand)
INTEGERS
\[\therefore \]\[Z=\{,4,3,2,1,0,1,2,3,4,\}\]
NUMBER LINE
Example: \[5<\text{ }5,7<\text{ }1,9<\text{ }3\]
Note: A number line drawn vertically, helps to know the heights above the and below the sea levels which are denoted by positive and negative signs respectively.
Absolute value of an integer
Example: \[+5=5,\,\,5=5,\,\,0=0\]
If x represents an integer then,
\[x=x,\] if \[x\] is positive or zero
\[=x\] if \[x\] is negative.
Fundamental Operations on Integers
Addition of two Integers:
Example 1: \[(2)+(1)=3.\]
We observe from the number line that \[(2)+(1)\]means '2' units to the left of '0' and '1' units to the left of \[(1)\] gives 3 units to left of zero. i.e.\[(2)+(1)=3.\]
Example 2: \[(2)+(1)=1.\]
We observe from the number line that \[\{(2)+1\}\]means '2' units to the left of zero and '1' unit right of \['2'\] gives '1' unit left of zero. i.e. \[(2)+1=1.\]
Subtraction of Integers
Example 1: \[72=5\]here, 5 gets the sign of 7 and on number line it is represented as follows.
i.e. \[72\]means 2 unit to left of 7.
Example 2: \[7(2)=7+2=5\]
ie. \[7(2)\] follows the rule of sign and becomes \[7+2\] which is equal to 2 unit to the right of \[7\] on number line.
Example 3: \[7(2)=9\]
i.e., \[72\]means 2 units to the left of\[7\]and gives\[9\].
Things to Remember
\[\times =+\] 
\[\,2\times 2=+\,4\] 
Sum of consecutive natural numbers \[=\frac{n\,(n+1)}{2}\] e.g, 1 + 2 + 3 + 4 + ???. + 50 
\[\times +=\] 
\[\,3\times 1=\,3\] 

\[+\times =\] 
\[4\times 2=\,8\]. 

\[+\times +=+\] 
\[2\times 6=12\] 
Solution: \[\frac{50\,(51)}{2}=25\times 51=1275\] 
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