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MATHS 5 Marks Questions

Number System · MP Board (MPBSE) STD 6 (Madhya Pradesh - English Medium). 12 questions.

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Question 15 Marks
Express each of the following as a Roman numeral:
S.No.
Numerical
$i$
$164$
$ii$
$195$
$iii$
$226$
$iv$
$341$
$v$
$475$
$vi$
$596$
$vii$
$611$
$viii$
$759$
Answer
We may write these numbers in Roman numerals as follows:
S.No.
Numerical
Roman numerals
$i$
$164$
$CLXIV$
$ii$
$195$
$CXCV$
$iii$
$226$
$CCXXVI$
$iv$
$341$
$CCCXLI$
$v$
$475$
$CDLXXV$
$vi$
$596$
$DXCVI$
$vii$
$611$
$DCXI$
$viii$
$759$
$DCCLIX$
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Question 25 Marks
Show that each of the following is meaningless. Give reason in each case.
$i.\ VC$
$ii.\ IL$
$iii.\ VVII$
$iv.\ IXX$
Answer
$i.\ VC$ is wrong because $V, L$ and $D$ are never subtracted.
$ii.\ IL$ is wrong because $I$ can be subtracted from $V$ and $X$ only.
$iii.\ VVII$ is wrong because $V, L$ and $D$ are never repeated.
$iv.\ IXX$ is wrong because $X ($ten$)$ must be placed before $IX ($nine$).$
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Question 35 Marks
Arrange the following numbers in ascending order: $1020304, 893245, 980134, 1021403, 893425, 1020216$
Answer
$893245, 893425$ and $980134$ are all $6-$digit numbers.
Among the three, $980134$ is the largest.
The other two numbers have the same digits, namely $8, 9$ and $3,$ at the lakhs, ten thousands and thousands places, respectively.
However, the digits at the hundreds place in $893245$ and $893425$ are $2$ and $4,$ respectively. Clearly, $2 < 4$
$\therefore 893245 < 893425$
$1020216, 1020304$ and $1021403$ are all $7-$digit numbers.
They have the same digits, namely $1, 0$ and $2,$ at the ten lakhs, lakhs and ten thousands places, respectively.
At the thousands place, $1021403$ has $1. $ The other two numbers have the digits $2 $ and $3$ at their hundreds places. Clearly, $2 < 3$
$\therefore 1020216 < 1020304$ The given numbers in ascending order are: $893245 < 893425 < 980134 < 1020216 < 1020304 < 1021403$
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Question 45 Marks
Arrange the following numbers in descending order: $63521047, 7354206, 63514759, 7355014, 102345680$
Answer
$102345680$ is a $9-$digit number. $63521047$ and $63514759$ are both $8-$digit numbers.
Both the numbers have the same digits, namely $6, 3$ and $5,$ at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in $63521047$ and $63514759$ are $2$ and $1,$ respectively.
Clearly, $2 > 1$
$\therefore 63521047 > 63514759$
$7355014$ and $7354206$ are both $7-$digit numbers.
Both the numbers have the same digits, namely $7, 3$ and $5$ at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in $7355014$ and $7354206$ are $5$ and $4,$ respectively.
Clearly, $5 > 4$
$\therefore 7355014 > 7354206$
The given numbers in descending order are:
$102345680 > 63521047 > 63514759 > 7355014 > 7354206$
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Question 55 Marks
Arrange the following numbers in descending order: $5032786, 23794206, 5032790, 23756819, 987876$
Answer
$23794206$ and $23756819$ are both $8-$digit numbers.
Both the numbers have the same digits, namely $2, 3$ and $7$ at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in $23794206$ and $23756819$ are $9$ and $5,$ respectively.
Clearly, $9 > 5$
$\therefore 23794206 > 23756819 $
$5032790$ and $5032786$ are both $7-$digit numbers.
Both the numbers have the same digits, namely $5, 0, 3, 2$ and $7,$ at the ten lakhs, lakhs, ten thousands, thousands and hundreds places, respectively.
However, the digits at the tens place in $5032790$ and $5032786$ are $9$ and $8,$ respectively.
Clearly, $9 > 8$
$\therefore 5032790 > 5032786 $
$987876$ is a $6-$digit number.
The given numbers in descending order are: $23794206 > 23756819 > 5032790 > 5032786 > 987876$
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Question 65 Marks
Arrange the following numbers in ascending order:
$56943201, 5694437, 56944000, 5695440, 56943300$
Answer
$5694437$ and $5695440$ are both $7-$digit numbers.
Both have the same digit, i.e., $5$ at the ten lakhs place.
Both have the same digit, i.e., $6$ at the lakhs place.
Both have the same digit, i.e., $9$ at the ten thousands place.
However, the digits at the thousand place in $5694437$ and $5695440$ are $4$ and $5,$ respectively.
Clearly, $4 < 5$
$\therefore 5694437 < 5695440$
$56943201, 56943300$ and $56944000$ are all $8-$digit numbers.
They have the same digit, i.e., $5$ at the crores place.
They have the same digit, i.e., $6$ at the ten lakhs place.
They have the same digit, i.e., $9$ at the lakhs place.
They have the same digit, i.e., $4$ at the ten thousands place.
However, at the thousands place, one number has $4$ while the others have $3 .$
$\therefore 56944000$ is the largest.
The other two numbers have $3$ and $2$ at their hundreds places.
Clearly, $2 < 3$
$\therefore 56943201 < 56943300$
The given numbers in ascending order are:
$5694437 < 5695440 < 56943201 < 56943300 < 56944000$
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Question 75 Marks
Arrange the following numbers in ascending order: $9873426, 24615019, 990357, 9874012, 24620010$
Answer
$990357$ is $6$ digit number.
$9873426$ and $9874012$ are both $7-$digit numbers.
Both the numbers have the same digits, namely $9, 8$ and $7,$ at the ten lakhs, lakhs and ten thousands places, respectively.
However, the digits at the thousands place in $9873426$ and $9874012$ are $3$ and $4,$ respectively.
Clearly, $4 < 7$
$\therefore 9873426 < 9874012$
$24615019$ and $24620010 $ are both $8-$digit numbers.
Both the numbers have the same digits, namely $2, 4$ and $6,$ at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in $24615019$ and $24620010$ are $2$ and $1,$ respectively.
Clearly, $1 < 2$
$\therefore 24615019 < 24620010$
The given numbers in ascending order are: $990357 < 9873426 < 9874012 < 24615019 < 24620010$
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Question 85 Marks
Arrange the following numbers in descending order: $199988, 1704382, 200175, 1702497, 201200, 1712040$
Answer
$1712040, 1704382$ and $1702497$ are all $7-$digit numbers.
The three numbers have the same digits, namely $1$ and $7,$ at the ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in $1712040, 1704382$ and $1702497$ are $1, 0$ and $0.$
$\therefore 1712040$ is the largest.
Of the other two numbers, the respective digits at the thousands place are $4$ and $2.$
Clearly, $4 > 2$
$\therefore 1704382 > 1702497 201200, 200175$ and $199988$ are all $6-$digit numbers.
At the lakhs place, we have $2 > 1.$
So, $199988$ is the smallest of the three numbers.
The other two numbers have the same digits, namely $2 $ and $0,$ at the lakhs and ten thousands places, respectively.
However, the digits at the thousands place in $201200$ and $200175$ are $1$ and $0,$ respectively.
Clearly, $1 > 0$
$\therefore 201200 > 200175$
The given numbers in descending order are: $1712040 > 1704382 > 1702497 > 201200 > 200175 > 199988$
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Question 95 Marks
Rewrite each of the following numerals with proper commas, using the international place$-$value chart.
Also, write the number name in the international system.
$i.\ 735821$
$ii.\ 6057894$
$iii.\ 56943821$
$iv.\ 7502093$
$v.\ 89350064$
$vi.\ 9070300$
Answer
Representation of the numbers on the international place$-$value chart:
Periods
Millions
Thousands
Ones
Place
Hundred
millions
Ten millions
Millions
Hundred thousands
Ten
thousands
Thousands
Hundreds
Tens
Ones
$HM$
$TM$
$M$
$H\ Th$
$T\ Th$
$Th$
$H$
$T$
$O$
$(i)$
 
 
 
$7$
$3$
$5$
$8$
$2$
$1$
$(ii)$
 
 
$6$
$0$
$5$
$7$
$8$
$9$
$4$
$(iii)$
 
$5$
$6$
$9$
$4$
$3$
$8$
$2$
$1$
$(iv)$
 
$3$
$7$
$5$
$0$
$2$
$0$
$9$
$3$
$(v)$
 
$8$
$9$
$3$
$5$
$0$
$0$
$6$
$4$
$(vi)$
 
$9$
$0$
$7$
$0$
$3$
$0$
$0$
$6$
 
 
Crore
Ten lakhs
Lakhs
Ten Thousand
Thousand
Hundred
Tens
Ones
The number names of the given numbers in the international system:
$i.\ 735,821 =$ Seven hundred thirty$-$five thousand eight hundred twenty$-$one.
$ii.\ 6,057,894 =$ Six million fifty$-$seven thousand eight hundred ninety$-$four.
$iii.\ 56,943,821 =$ Fifty$-$six million nine hundred forty$-$three thousand eight hundred twenty$-$one.
$iv.\ 37,502,093 =$ Thirty$-$seven million five hundred two thousand ninety$-$three.
$v.\ 89,350,064 =$ Eighty$-$nine millions three hundred fifty thousand sixty$-$four.
$vi.\ 90,703,006 =$ Ninety million seven hundred three thousand and six.
 
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Question 105 Marks
Arrange the following numbers in descending order:
$190909, 1808088, 16060666, 16007777, 181888, 1808090$
Answer
$16060666$ and $16007777$ are both $8-$digit numbers.
Both the numbers have the same digits, namely $1, 6$ and $0,$ at the crores, ten lakhs and lakhs places, respectively.
However, the digits at the ten thousands place in $16060666$ and $16007777$ are $6$ and $0, $ respectively.
Clearly, $6 > 0$
$\therefore 16060666 > 16007777$
$1808090$ and $1808088$ are both $7-$digit numbers.
Both the numbers have the same digits, namely $1, 8, 0, 8$ and $0,$ at the ten lakhs, lakhs, ten thousands, thousands and hundreds places, respectively.
However, the digits at the tens place in $1808090$ and $1808088$ are $9$ and $8,$ respectively.
Clearly, $9 > 8$
$\therefore 1808090 > 1808088$
$190909$ and $181888$ are both $6-$digit numbers.
Both the numbers have the same digit, $1,$ at the lakhs place.
However, the digits at the ten thousands place in $190909$ and $181888$ are $9$ and $8,$ respectively.
Clearly, $9 > 8$
$\therefore 190909 > 181888$
Thus, the given numbers in descending order are:
$16060666 > 16007777 > 1808090 > 1808088 >190909 > 181888$
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Question 115 Marks
Write each of the following as a Hindu-Arabic numeral:
S.No.
Roman numeral
$i$
$XXVII$
$ii$
$XXXIV$
$iii$
$XLV$
$iv$
$LIV$
$v$
$LXXIV$
$vi$
$XCI$
$vii$
$XCVI$
$viii$
$CXI$
$ix$
$CLIV$
$x$
$CCXXIV$
$xi$
$CCCLXV$
$xii$
$CDXIV$
$xiii$
$CDLXIV$
$xiv$
$DVI$
$xv$
$DCCLXVI$
Answer
We can write the given Roman numerrals in Hindu-Arabic numerals as follows:
S.No.
Roman numeral
 Hindu-Arabic
$i$
$XXVII$
 $27$
$ii$
$XXXIV$
 $34$
$iii$
$XLV$
 $45$
$iv$
$LIV$
 $54$
$v$
$LXXIV$
 $74$
$vi$
$XCI$
 $91$
$vii$
$XCVI$
 $96$
$viii$
$CXI$
 $111$
$ix$
$CLIV$
 $154$
$x$
$CCXXIV$
 $224$
$xi$
$CCCLXV$
 $365$
$xii$
$CDXIV$
 $414$
$xiii$
$CDLXIV$
 $464$
$xiv$
$DVI$
 $506$
$xv$
$DCCLXVI$
 $766$
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Question 125 Marks
Express each of the following as a Roman numeral:
S.No.
Numerical
$i$
$2$
$ii$
$8$
$iii$
$14$
$iv$
$29$
$v$
$36$
$vi$
$43$
$vii$
$54$
$viii$
$61$
$ix$
$73$
$x$
$81$
$xi$
$91$
$xii$
$95$
$xiii$
$99$
$xiv$
$105$
$xv$
$114$
Answer
We may write these numbers as given below:
S.No.
Numerical
Roman numeral
$i$
$2$
$II$
$ii$
$8$
$VIII$
$iii$
$14$
$XIV$
$iv$
$29$
$XXIX$
$v$
$36$
$XXXVI$
$vi$
$43$
$XLIII$
$vii$
$54$
$LIV$
$viii$
$61$
$LXI$
$ix$
$73$
$LXXIII$
$x$
$81$
$LXXXI$
$xi$
$91$
$XCI$
$xii$
$95$
$XCV$
$xiii$
$99$
$XCIX$
$xiv$
$105$
$CV$
$xv$
$114$
$CXIV$
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