Solutions - Exercise 1 (B) | Number System | Class 6 Mathematics | Selina Concise Mathematics - Middle School.
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📂 Chapter 1 - Exercise 1 (B).
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# Let's Discuss :
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# Comparing Numbers :
In order to compare two numbers, we follow the rules given below :
Rule 1 : If the two numbers have different numbers of digits then the number with more number of digits is greater.
E.g. In numbers 54932 and 942362, The number 942362 is greater as it has more number of digits (i.e. 6 digits).
Rule 2 : If two numbers have equal number of digits then we compare the place value of digits starting from leftmost place in both the numbers.
E.g. In numbers 53421 and 54321, The number of digits are same (i.e. 5 digits). Here, 54321 is greater as the digit on the thousands place is greater (i.e. 4000).
Rule 3 : If two numbers have equal number of digits then we compare the place value of digits starting from leftmost place in both the numbers using place value chart (table).
| Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|
| 5 | 4 | 0 | 2 | 7 | 6 |
| 3 | 6 | 9 | 9 | 9 | 8 |
Here, The number 540276 is greater as it digit on the Lakhs place is greater.
# Forming Smallest and Greatest number using Digits :
We can form different numbers from a given set of digits by arranging the given digits in various places.
(i) To form Greatest number : To form the greatest number arrange the digits in Descending order.
(ii) To form Smallest number : To form the smallest number arrange the digits in Ascending order.
📌Note : Descending order means greater to smaller and Ascending order means smaller to greater.
(a) When the given digits do not include 0.
We can form different numbers from a given set of digits by arranging the given digits in various places.
E.g.
Given Digits : 5, 4, 6, 3, 9
(i) To form Greatest number : Arrange the digits in Descending order like 96543.
(ii) To form Smallest number : Arrange the digits in Ascending order like 34569.
(b) When the given digits include 0.
We can form different numbers from a given set of digits by arranging the given digits in various places.
E.g.
Given Digits : 5, 4, 0, 3, 9
(i) To form Greatest number : Arrange the digits in Descending order like 95430.
(ii) To form Smallest number : Arrange the digits in Ascending order like 30459.
📌Note : To form the smallest number, The digit '0' should not be placed at extreme left, but it can be placed at second place from the left side.
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-- EXERCISE - 1 (B) --
Q1. Which is greater ?
(i) 537 or 98
Solution :
The first number is 537 i.e. 500 + 30 + 7
The second number is 98 i.e. 90 + 8
Here,
The first number 537 has high place value i.e. 500
Therefore,
537 is the greater number.
Ans. 537
(ii) 2428 or 529
Solution :
The first number is 2428 i.e. 2000 + 400 + 20 + 8
The second number is 529 i.e. 500 + 20 + 9
Here,
The first number 2428 has high place value i.e. 2000
Therefore,
2428 is the greater number.
Ans. 2428
(iii) 259467 or 1035729
Solution :
The first number is 259467 i.e. 2,00,000 + 50,000 + 9,000 + 400 + 60 + 7
The second number is 1035729 i.e. 10,00,000 + 30,000 + 5000 + 700 + 20 + 9
Here,
The second number 1035729 has high place value i.e. 10,00,000
Therefore,
1035729 is the greater number.
Ans. 1036729
(iv) 63520 or 63250
Solution :
The first number is 63520 i.e. 60,000 + 3000 + 500 + 20
The second number is 63250 i.e. 60,000 + 3000 + 200 + 50
Here,
The first number 63520 has higher Hundreds place value i.e. 500
Therefore,
63520 is the greater number.
Ans. 63520
Q2. Which is smaller ?
(i) 428 or 437
Solution :
The first number is 428 i.e. 400 + 20 + 8
The second number is 437 i.e. 400 + 30 + 7
Here,
The first number 428 has smaller Tens place value i.e. 20
Therefore,
428 is the smaller number.
Ans. 428
(ii) 2497 or 2597
Solution :
The first number is 2497 i.e. 2000 + 400 + 90 + 7
The second number is 2597 i.e. 2000 + 500 + 90 + 7
Here,
The first number 2497 has smaller Hundreds place value i.e. 400
Therefore,
2497 is the smaller number.
Ans. 2497
(iii) 3297 or 3596
Solution :
The first number is 3297 i.e. 3000 + 200 + 90 + 7
The second number is 3596 i.e. 3000 + 500 + 90 + 6
Here,
The first number 3297 has smaller Hundreds place value i.e. 200
Therefore,
3297 is the smaller number.
Ans. 3297
(iv) 380362 or 381007
Solution :
The first number is 380362 i.e. 3,00,000 + 80,000 + 300 + 60 + 2
The second number is 381007 i.e. 3,00,000 + 81,000 + 7
Here,
The first number 380362 has smaller Thousands place value i.e. 80,000
Therefore,
380362 is the smaller number.
Ans. 380362
Q3. By making a suitable chart, compare :
(i) 540276 and 369998
Solution :
| Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|
| 5 | 4 | 0 | 2 | 7 | 6 |
| 3 | 6 | 9 | 9 | 9 | 8 |
The first number is 540276 i.e. 5,00,000 + 40,000 + 200 + 70 + 6
The second number is 369998 i.e. 3,00,000 + 69,000 + 900 + 90 + 8
Here,
The second number 369998 has smaller Lakhs place value i.e. 3,00,000
Therefore,
369998 is the smaller number.
Ans. 369998
(ii) 6983245 and 6893254
Solution :
| Ten Lakhs (TL) | Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|---|
| 6 | 9 | 8 | 3 | 2 | 4 | 5 |
| 6 | 8 | 9 | 3 | 2 | 5 | 4 |
The first number is 6983245 i.e. 60,00,000 + 9,00,000 + 83,000 + 200 + 40 + 5
The second number is 6893245 i.e. 60,00,000 + 8,00,000 + 93,000 + 200 + 50 + 4
Here,
The second number 6893245 has smaller Lakhs place value i.e. 8,00,000
Therefore,
6893254 is the smaller number.
Ans. 6893254
Q4. Compare the numbers written in the following table writing them in ascending order :
| Crores (C) | Ten Lakhs (TL) | Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|---|---|
| 5 | 4 | 3 | 2 | 9 | 7 | 2 | |
| 2 | 3 | 1 | 0 | 6 | 2 | 9 | 3 |
| 5 | 2 | 2 | 3 | 7 | 9 | 1 | |
| 2 | 3 | 1 | 8 | 2 | 6 | 3 | 4 |
| 5 | 4 | 3 | 4 | 4 | 7 | 8 | 2 |
Solution :
Ascending Order - 52,23,791 < 54,32,972 < 2,31,06,293 < 2,31,82,634 < 5,43,44,782.
Q5. Use a place value chart to compare the given numbers and write them in descending order : 543287 ; 5482900 ; 2732940 ; 43877 ; 78396 and 4999.
Solution :
| Ten Lakhs (TL) | Lakhs (L) | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (o) |
|---|---|---|---|---|---|---|
| 5 | 4 | 3 | 2 | 8 | 7 | |
| 5 | 4 | 8 | 2 | 9 | 0 | 0 |
| 2 | 7 | 3 | 2 | 9 | 4 | 0 |
| 4 | 3 | 8 | 7 | 7 | ||
| 7 | 8 | 3 | 9 | 6 | ||
| 4 | 9 | 9 | 9 |
Descending order - 54,82,900 > 27,32,940 > 5,43,287 > 78,396 > 43,877 > 4,999
Q6. Find the smallest and the greatest numbers in each of the cases given below :
(i) 983, 5754, 84 and 5942
Solution :
The first number is 983 i.e. 900 + 80 + 3
The second number is 5754 i.e. 5000 + 700 + 50 + 4
The third number is 84 i.e. 80 + 4
The fourth number is 5942 i.e. 5000 + 900 + 40 + 2
Here,
The third number 84 has smallest Hundreds place value i.e. 000
The fourth number 5942 has greatest Thousands and Hundreds place value i.e. 5000 + 900
Therefore,
84 is the smallest number and 5942 is the greatest number.
Ans. Smallest = 84 and Greatest = 5942
(ii) 32849, 53628, 5499 and 54909.
Solution :
The first number is 32849 i.e. 30,000 + 2000 + 800 + 40 + 9
The second number is 53628 i.e. 50,000 + 3000 + 600 + 20 + 8
The third number is 5499 i.e. 5000 + 4000 + 90 + 9
The fourth number is 54909 i.e. 50,000 + 4000 + 900 + 9
Here,
The third number 5499 has smallest Ten Thousands place value i.e. 00,000
The fourth number 54909 has greatest Ten Thousands and Thousands place value i.e. 50,000 + 4000
Therefore,
5499 is the smallest number and 54909 is the greatest number.
Ans. Smallest = 5499 and Greatest = 54909
Q7. Form the greatest and the smallest 4-digit numbers using the given digits, without repetition :
📌 Note : To form the greatest number, we need to arrange these digits in descending order of their face value and to form the smallest number, we need to arrange these digits in ascending order of their face value.
(i) 3, 7, 2 and 5
Solution :
Smallest number : 2357
Greatest number : 7532
(ii) 6, 1, 4 and 9
Solution :
Smallest number : 1469
Greatest number : 9641
(iii) 7, 0, 4 and 2
Solution :
Smallest number : 2047
Greatest number : 7420
(iv) 1, 8, 5 and 3
Solution :
Smallest number : 1358
Greatest number : 8531
(v) 9, 6, 0 and 7
Solution :
Smallest number : 6079
Greatest number : 9760
(vi) 9, 5, 8 and 1
Solution :
Smallest number : 1589
Greatest number : 9851
Q8. Form the greatest and the smallest 4-digit numbers using any four different digits, with the condition that digit 5 is always at the ten's place.
Solution :
To form greatest number :
Let the 4 digits be 9, 8, 7, 5
Greatest number with 5 at the ten's place = 9857
To form smallest number :
Let the 4 digits be 0, 1, 2, 5
Smallest number with 5 at the ten's place = 1052
Q9. Form the largest number with the digits 2, 3, 5, 9, 6 and 0, without repetition of any digit.
Solution :
Largest number = 965320
Q10. Write the smallest and the greatest 4-digit numbers, without repetition of any digit.
Solution :
To form greatest number :
Let the 4 digits be 9, 8, 7, 6
Greatest number without repetition of digits = 9876
To form smallest number :
Let the 4 digits be 0, 1, 2, 3
Smallest number without repetition of digits = 1023
Q11. Find the sum of the largest and the smallest four-digit numbers.
Solution :
Largest 4 digit number = 9999
Smallest 4 digit number = 1000
Sum of numbers = 9999 + 1000 = 10,999
Ans. 10,999
Q12. Form the greatest and the smallest five-digit numbers with 8 in the hundred's place and with all the digits different.
Solution :
To form greatest number :
Let the 5 digits be 9, 8, 7, 6, 5
Greatest number with 8 at the hundred's place = 97865
To form smallest number :
Let the 5 digits be 0, 1, 2, 3, 8
Smallest number with 8 at the hundred's place = 10823
Q13. Find the difference between the smallest and the greatest six-digit numbers.
Solution :
Greatest 6 digit number = 9,99,999
Smallest 6 digit number = 1,00,000
Difference = 999999 - 100000 = 8,99,999
Ans. 8,99,999
Q14.
(i) How many four-digit numbers are there between 999 and 3000 ?
Solution :
Smallest 4 digit number between 999 and 3000 = 1000
Largest 4 digit number between 999 and 3000 = 3000
Difference = 3000 - 1000 = 2000.
Ans. 2000
(ii) How many four-digit numbers are there between 99 and 3000 ?
Solution :
Smallest 4 digit number between 99 and 3000 = 1000
Largest 4 digit number between 999 and 3000 = 3000
Difference = 3000 - 1000 = 2000.
Ans. 2000
Q15. How many four-digit numbers are there between 1001 and 4000 ?
Solution :
Smallest 4 digit number between 1001 and 4000 = 1002
Largest 4 digit number between 1001 and 4000 = 4000
Difference = 4000 - 1002 = 2998
Ans. 2998
Q16. Write all the possible three-digit numbers using the digits 3, 6 and 8, if repetition of any digit is not allowed.
Solution :
All possible 3 digit numbers without repetition = 368, 386, 638, 683, 836, 863.
Q17. Form the greatest and the smallest 4-digit numbers using the digits 5, 4, 7 and 9 (without repeating the digits) and with the condition that :
(i) 7 is at the ones place.
Solution :
Smallest 4 digit number without repetition = 4597
Greatest 4 digit number without repetition = 9547
(ii) 9 is at the tens place.
Solution :
Smallest 4 digit number without repetition = 4597
Greatest 4 digit number without repetition = 7594
(iii) 4 is at the hundreds place
Solution :
Smallest 4 digit number without repetition = 5479
Greatest 4 digit number without repetition = 9475
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