3 Marks Question

Question 13 Marks

Arrange the following numbers in descending order: $54796203, 4675238, 63240613, 5125648, 589623$

Answer

$63240613$ and $54796203$ are both eight-digit numbers.
At the crores place, one number has $6$, while the second number has $5.$
Clearly, $5 < 6$
$\therefore 63240613 > 54796203 \ 5125648$ and $4675238$ are both seven-digit numbers.
However, at the ten lakhs place, one number has $5$, while the second number has $4.$
Clearly, $4 < 5$
$\therefore 5125648 > 4675238 \ 589623$ is a six-digit number.
The given numbers in descending order are: $63240613 > 54796203 > 5125648 > 4675238 > 589623$

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Question 23 Marks

Write the Hindu-Arabic numeral for each of the following:

S.No.	Roman numeral
$i$	$CCXLII$
$ii$	$CDLXV$
$iii$	$LXXVI$
$iv$	$DCCXLI$
$v$	$XCIV$
$vi$	$CXCIX$

Answer

S.No.	Roman numeral	Hindu-Arabic
$i$	$CCXLII$	$CCXLII = 100 + 100 + (50 - 10) + 2 = 242$
$ii$	$CDLXV$	$CDLXV = (500 - 100) + 50 + 10 + 5 = 465$
$iii$	$LXXVI$	$LXXVI = 50 + 10 + 10 + 6 = 76$
$iv$	$DCCXLI$	$DCCXLI = 500 + 100 + 100 + (50 - 10) + 1 = 741$
$v$	$XCIV$	$XCIV = (100 - 10) + 4 = 94$
$vi$	$CXCIX$	$CXCIX = 100 + (100 - 10) + 9 = 199$

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Question 33 Marks

Write the largest and smallest numbes using each of the digits $1, 4, 6, 8, 0$ only once and find their difference.

Answer

The largest number using each of the digits: $1, 4, 6, 8$ and $0,$ is $86410$.
The smallest number using each of the digits: $1, 4, 6, 8$ and $0,$ is $10468.$
$\therefore$ Required difference $= 86410 - 10468 = 75942$

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Question 43 Marks

Arrange the following numbers in ascending order: $700087, 8014257, 8015032, 10012458, 8014306$

Answer

$700087$ is $6-$digit number. $8014257, 8014306$ and $8015032$ are all $7-$digit numbers.
They have the same digits, namely $8, 0$ and $1,$ at the ten lakhs, lakhs and ten thousands places, respectively.
But, at the thousands place, one number has $5$ while the other two numbers have $4.$
Here, $801503$ is the largest.
The other two numbers have $2$ and $3$ at their hundreds places.
Clearly, $2 < 3$
$\therefore 8014306 < 8015032 \ 10012458$ is an $8-$digit number.
The given numbers in ascending order are: $700087 < 8014257 < 8014306 < 8015032 < 10012458$

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Question 53 Marks

Arrange the following numbers in ascending order: $3903216, 19430124, 864572, 6940513, 16531079$

Answer

We have, $864572$ is a $6-$digit number.
$3903216$ and $6940513$ are seven-digit numbers.
At the ten lakhs place, one number has $3$, while the second number has $6.$
Clearly, $3 < 6$
$\therefore 3903216 < 6940513 \ 16531079$ and $19430124$ are eight-digit numbers.
At the crores place, both the numbers have the same digit, namely $1.$
At the ten lakhs place, one number has $6$, while the second number has $9.$
Clearly, $6 < 9$
$\therefore 16531079 < 19430124$
The given numbers in ascending order are: $864572 < 3903216 < 6940513 < 16531079 < 19430124$

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Question 63 Marks

How many $7$-digit numbers are there in all?

Answer

The largest seven-digit number $= 9999999$
The smallest seven-digit number $= 1000000$
Number of all seven-digits numbers $= (9999999 - 1000000) + 1$
$= 899999 + 1$
$= 9000000$
Hence, there is a total of ninety lakh $7-$digit numbers.

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Question 73 Marks

Write the Roman numeral for each of the following:

S.No.	Numerical
$i$	$84$
$ii$	$99$
$iii$	$145$
$iv$	$406$
$v$	$519$

Answer

S.No.	Numerical	Roman numeral
$i$	$84$	$84 = 50 + 30 + 4 = LXXXIV$
$ii$	$99$	$99 = 90 + 9 = XCIX$
$iii$	$145$	$145 = 100 + (50 - 10) + 5 = CXLV$
$iv$	$406$	$406 = 400 + 6 = CDVI$
$v$	$519$	$519 = 500 +10 + 9 = DXIX$

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Question 83 Marks

Write each of the following in figures in the international place$-$value chart:
$i.\ $Thirty million one hundred five thousand sixty$-$three.
$ii.\ $Fifty$-$two million two hundred five thousand six.
$iii.\ $Five million five thousand five.

Answer

Periods	Millions			Thousands			Ones
Place	Hundred millions	Ten millions	Millions	Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
Place	$HM$	$TM$	$M$	$H Th$	$T Th$	$Th$	$H$	$T$	$O$
$(i)$		$3$	$0$	$1$	$0$	$5$	$0$	$6$	$3$
$(ii)$		$5$	$2$	$2$	$0$	$5$	$0$	$0$	$6$
$(iii)$			$5$	$0$	$0$	$5$	$0$	$0$	$5$

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