Number System
Sample Questions
1)
a)10 tens = 10 * 10
= 100
= 1hundred
b) 100 tens = 100 * 10
= 1000
= 1 thousand
c) 1000 ones = 1000 * 1
= 1000
= 1 thousand
2) Using digits 5 , 0 , 3 , 8 , 1 each only once
a) Smallest 3 digit number
First, we have to check the smallest number
the smallest number among the given numbers 5, 0, 3, 8, 1 is 0
but if we write 0 in the first place then the three-digit number will become a two-digit number.
so the next smallest number is 1
write1 in the first place
now for the second place, we can write 0
for the third place, the next smallest number is 3
hence the smallest three-digit number among the given numbers is 103
b) Smallest five-digit number having 1 at hundreds place
given 1 at hundreds place
so, TTh Th H T O
1
at TTh place, 0 is not possible (if we write 0 then it will become 4 digit number)
1 is also not possible because given that it must be in the hundred place
the next smallest is 3
TTh Th H T O
3 1
TTh Th H T O
3 0 1
TTh Th H T O
3 0 1 5
TTh Th H T O
3 0 1 5 8
Hence the smallest 5 digit number among the given number and 1 at hundred places is 30158
3) Using the digits 0 , 3 , 9 , 2 , 4 each only once
a) largest 4 digit number
here, we have to write from the largest number
Th H T O
9
Th H T O
9 4
Th H T O
9 4 3
Th H T O
9 4 3 2
hence the largest four-digit number among given numbers is 9432
b) largest 5 digit number having 9 at tens place
given, 9 at tens place
so TTh Th H T O
9
TTh Th H T O
4 9
TTh Th H T O
4 3 9
TTh Th H T O
4 3 2 9
TTh Th H T O
4 3 2 9 0
Hence the largest 5 digit number having 9 at tens place is 43290
4) Write in words
a) 78609 = Seventy eight thousand six hundred and nine
b) 65079 = Sixty five thousand seventy nine
5)
a) The greatest 5 digit number with all digits different and 4 at tens place is
TTh Th H T O
4
TTh Th H T O
9 8 7 4 6
hence the greatest 5 digit number is 98746
b) The smallest 5 digit number with all digits different and 8 at hundred places is
TTh Th H T O
8
TTh Th H T O
9 7 8 6 5
Hence the smallest 5 digit number with all digits different and 8 at hundred places is 97865
6) Expanded form of 38092 is 30000 + 8000 + 0 + 90 + 2
7) Compare
a) DCCCLXXXIX _____ CMLIX
I - 1 : V - 5 : X - 10 : L - 50 : C - 100 : D - 500 : M - 1000
D C C C L X X X IX
500 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 9 = 889
CM L IX
900 + 50 + 9 = 959
DCCCLXXXIX ( 889 ) < CMLIX ( 959)
b) CDXXIV _____ CCCXXIV
CD X X IV
400 + 10 + 10 + 4 = 424
C C C X X IV
100 + 100 + 100 + 10 + 10 + 4 = 324
CDXXIV (424) > CCCXXIV (324)
8) Place Value : Place value is the value of each digit in a number
Face value : Face value of a number is the value of the number itself
a) In number 35687 the place and face value of 6 is
place value of 6 is 600
face value of 6 is 6
b) In number 87312, which digit has same place value and face value?
the place value of any number in the units place is the number itself
hence place value = face value = 2
9) Arrange in Ascending and descending order
38790, 39087 , 37908 , 30789 , 38079
Ascending order : Small to big
30789 , 37908 , 38079 , 38790 , 39087
Descending order : big to small
39087, 38790, 38079 , 37908 , 30789
10 ) Seventy five thousand five hundred is same as 75500
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