Category : 6th Class
Knowing our Numbers
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Indian System: 73, 32, 54,329
International System: 733,254,329
Note: A Comma is inserted each period in both the systems.
Indian system |
1 lakh |
10 lakhs |
1 Crore |
10 Cores |
100 Cores |
International System |
Hundred Thousands |
1 Million |
10 Millions |
100 Millions |
1 Billon |
e.g., 5340769 = 53, 40,769
e.g., 5340769 = 5,340,769
The face value of a digit is the value of the digit itself.
e.g. In 7308, the face value of 7 is 7.
Place value = Face value \[\times \]Value of its place in the place value chart
e.g., (1) In 39065, the face value of 9 is 9 and the place value of 9 is 9 x 1000 = 9000.
e.g., (2) In 7308, the face value of 3 is 3; while its place value is 300.
Note: Place value of zero(0) at any place is always zero. Thus, the face value and the place value of zero are 0.
To write a number in expanded form, start from the left-most digit. Write the digit in the given number followed by as many zeroes as the number of digits to its right. Place a + sign before writing the next digit. Continue this until the right-most digit is written.
e.g.. The expanded form of
906352146 = 900000000 + 00000000 + 6000000 + 300000 + 50000 + 2000 + 100 +40+6
No. of digits |
Smallest |
Largest |
1 |
0 |
9 |
2 |
10 |
99 |
3 |
100 |
999 |
4 |
1000 |
9999 |
5 |
10000 |
99999 |
6 |
100000 |
999999 |
Note: To write the smallest of \[\mathbf{'n'}\]digits (other than 1), write 1 followed by (n - 1) zeroes. To write the largest number of \[\mathbf{'n'}\] digits, write \[\mathbf{'n'}\] 9 s.
(i) Count the number of places. The number with more number of places is greater and that with less places is smaller.
(ii) If the number of places is equal then compare the value of the digit present from place to place from left to right in both the numbers. The number with greater value is greater.
Roman numeral |
I |
V |
X |
L |
C |
D |
M |
Hindu- Arabic Numeral |
1 |
5 |
10 |
50 |
100 |
500 |
1000 |
Rule 1: If a symbol is repeated, its value is added as many times as it occurs.
Note: A Symbol is never repeated for more than three times. The symbols V,L and D are never repeated i.e., only I ,X,C and M can be repeated.
Rule 2: When a symbol of smaller value is written to the right of a symbol of greater value, its value is added to the value of the greater symbol.
e.g., XI =10+1 =11; LXV= 50+10+5=65
Rule 3: When a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.
e.g., XC=100-10=90; IV=5-1 =4
Note: The symbols V,L and D are n ever subtracted.\[\mathbf{'I'}\]Can be subtracted from V and X only once.\[\mathbf{'X'}\] can be subtracted from L and C only once.\[\mathbf{'C'}\]can be subtracted from D and M only once.
With the help of the symbols I, V, X, L and C, we can write numbers upto 399.
Rule4: When a smaller numeral is placed between two larger numerals, it is always subtracted from the larger numeral immediately following it.
e.g., CXIV = 100 + 10 + (5 - 1) = 114.
Rule 5: When a bar is placed over a numeral, it is multiplied by 1000.
e.g., \[\overline{V}\]= 5000, z\[\overline{L}\]= 50000, \[\overline{IV}\]= 4000.
e.g., 4117 can be approximated to 4100 (to the nearest hundred)
4117 can be approximated to 4000 (to the nearest thousand)
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