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NUMBER SYSTEM
1. Write the numeral for each of the following :
(i) Six thousand four hundred eighteen
(ii) Twelve thousand sixteen
(iii) Three lakh twenty-four thousand six hundred ninety
(iv) Five lakh five thousand five hundred five
(v) Two crore thirty-five lakh seven thousand five hundred
Ans. (i) 6, 418 (ii) 12, 016 (iii) 3, 24, 690 (iv) 5, 05, 505 (v) 2, 35, 07, 500
2. Write the number name for each of the following numerals :
(i) 17, 582
(ii) 2, 36, 406 (iii) 9,09,009
(iv) 27, 10, 300
(v)
30, 14,023 (vi) 7, 07, 30,500
Ans. (i) Seventeen thousand five hundred eighty two.
(ii) Two lakh thirty six thousand four hundred six
(iii) Nine lakh nine thousand nine.
(iv) Twenty-seven lakh ten thousand three hundred.
(v) Thirty lakh fourteen thousand twenty three.
(vi) Seven crore seven lakh thirty thousand five hundred,
3 .(i) Write the place value of 7 in 673048.
(ii) Write the place value of 4 in 274562.
(iii) Write the place-value of 8 in 802316.
(iv) Write the place value of 6 in 280614.
Ans. (i) Place-value of 7 in 673048 = 7 × 10000 = 70000
(ii) Place-value of 4 in 274562 = 4 × 1000 = 4000.
(iii) Place-value 8 in 802316 = 8 × 100000 = 800000
(iv) Place-value of 6 in 280614 = 6 × 100 = 600.
4. Find the difference in the place values of two sixes in the numeral 674613.
Ans. 674613
Place value of two 6’s in 67413 are 600 and 600000
6 × 100 = 600
6 × 100000 = 600000 ∴ Required difference = 600000 – 600 = 599400.
5. Find the difference in the place value and the face value of 9 in the numberal 86906.
Ans. Place value of 9 in 86906 = 9 × 100
Face-value of 9 in 86906 = 9
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Class - VI Mathematics
∴ Required difference = 900 – 9 = 891.
6. How many four-digit numbers are there ?
Ans. Number of all 4-digit numbers = (9999 – 1000)+1 = 8999 + 1 = 1= 9000.
7. How many five digit numbers are there ?
Ans. Number of all 5-digit numbers = (99999 – 10000)+1 = 89999 + 1 = 90000
8. (i) Write all possible three digit numbers using the digits 1, 2 and 7, when repetition of digits is not allowed.
(ii) Write all possible three-digit numbers using the digits 1, 0 and 7, taking each
digit only once in each number.
Ans. (i) The required numbers are 127, 217, 271, 721, 172, and 712,
(ii) The required numbers are 170, 710, 701 and 107.
9. Write each of the following numbers in expanded form:
(i) 2,37,050
(ii)
4,09,108
(iii) 23,14,502
(iv) 1, 39,56,708 (v)
12,06,07,917
Ans. (i) 2, 37,050 = (2× 100000) + (3 × 10000) + (7× 1000) + (0 × 100) + (5 × 10)
+ (0 × 1)
(ii) 409109 = (4 + 100000) + (0 × 10000 + (1 × 100) + (0× 10) + (8 × 1)
(iii) 23,14,502 = (2 × 1000000) + (3 × 100000) + (1 × 10000) + (4 × 1000) +
(5 × 100) + (0 × 10) + ( 2 × 1)
(iv) 1,39,56,708 = (1 × 10000000) + (3 × 1000000) + (9 × 100000) + (5 ×
10000) + (6 × 1000) + (7 × 100) + (0 × 10) + (8 × 1)
(v) 12,06,07,917 = (1 × 100000000) + (2 × 10000000) + (0 × 1000000) + (6 ×
100000) + (0 × 10000) + (7 × 1000) + ( 9 × 100) + (1 × 10) + (7 × 1)
10. Write each of the following numbers in short form :
(i) (9 × 1000) + (7 × 100) + (0 × 10) + ( 6 × 1)
(ii) (7 × 10000) + (3 × 100)+ (4 × 10)
(iii) (5 × 100000) + (2 × 10000) + (0 × 1000) + (5 × 100) + (0 × 10) + ( 7 × 1)
(iv) (3 × 1000000) + (5 × 100000) + (0 × 10000) + (7 × 1000) + (0 × 100) +
(6 × 10) + (5 × 1)
Ans. (i) 9000 + 700 + 0 + 6 = 9,706
(ii) 70000 + 300 + 40 = 70, 340
(iii) 500000 + 20000 + 0 + 500 + 0 + 7 = 5, 20, 507
(iv) 30000000 + 500000 + 0 + 7000 + 0 + 60 + 5 = 35, 07, 065
11. Write the successor of each of the following numbers :
(i) 29099 (ii) 3559999 (iii) 9999299
Ans. (i) Successor of 29099 = 29099 + 1 = 29100.
(ii) Succession of 3559999 = 3559999 + 1 3560000.
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(iii) Successor of 9999 299 = 9999300.
12. Write the predecessor of each of the following number :
(i) 120000 (ii) 2860100 (iii) 6810000
Ans. (i) Predecessor of 120000 = 120000 – 1 = 119999.
(ii) Predecessor of 2860100 = 2860100 – 1 = 2860099.
(iii) Predecessor of 6810000 = 6810000 – 1 = 6809999.
13. Write down three consecutive whole numbers just preceding 6510001.
Ans. Three consecutive whole number just preceding 6510001 are 650998, 6509999
and 6510000.
14. Which is greater : 96580734 or 96721643 ?
Ans. Let us arrange the given numbers in the place value chart. Both the numbers have 8
digits. At the crores place, both have the same digit namely, 9. At the ten lakhs place,
both the numbers again have the same digit namely, 6.
But, at the lakhs place, the first number has 5 while the second has 7.
Clearly, 7 > 5. ∴96721643 > 96580734.
15. Arrange the following numbers in ascending order : 14865710, 20507106, 3000
8215, 2786789 and 2876879.
Ans.Given numbers in ascending order as : 2786789, 2876879, 14865710, 20507106,
30008215.
16. Write all whole numbers between 400 and 500 which do not change if the order of
the digits is reversed.
Ans. Required numbers are : 404, 414, 424, 434, 444, 454, 464, 474, 484, 494.
17. Arrange the following numbers in descending order : 62790568, 627905480,
62791023, 627905623, 627909931
T - C C T -L L T - Th Th H T O
Ans. Let us arrange the given numbers in the place-value
6
2 7
0 5 6 8
9
chart .
2
0
6
7 9
5 4 8 0
6
2 7
1 0 2 3
9
The given numbers in decreasing order
2
5 6 2 3
6
7 9
0
627905623 > 627905480 > 62791023 > 62790931
2
9
2 9
0 9 3 1
> 62790568.
18. Write in figures as well as in words :
(i) Smallest number of six digits.
(ii) Largest number of six digits.
(iii) Smallest number of eight digits.
(iv) Largest number of eight digits.
Ans. (i) 100000, one lakh
(ii) 999999, nine lakh ninety-nine thousand nine hundred ninety nine.
(iii) 10000000, one crore
(iv) 99999999, nine crore ninety nine lakh ninety nine thousand nine hundred ninety
nine.
19. Write the smallest 4-digit number using each of the following digits only once:
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Question Bank
Class - VI Mathematics
(i) 0, 1, 3 and 6
(ii) 4, 7, 3 and 5
Ans (i) Required 4-digit number is 1036.
(ii) So, required number is 3457.
20. (i) Write the smallest 3-digit number using digits 0 and 5, repeating 5 two times.
(ii) Write the smallest 4-digit number using digits 5, 8 and 2 repeating 8 two times.
Ans. (i) Required number is 505.
(ii) So, required number is 2588.
21. (i) Write the greatest 4-digit number using digits 7, 2 and 5, repeating 5 two
(ii) Write the greatest 4-digit number using digits 1, 6 and 0, repeating 6 two times.
Ans. (i) So, required number = 7552. (ii) So required number = 6610.
22. Write the greatest 5-digit number using the digits 8,0 and 4.
Ans. Required greatest 5-digit number using the digits 8, 0 and 4 is 88840.
23. Write the smallest 6-digit number using the digits 1, 7 and 8.
Ans. Required smallest 6-digit number using the digits 1, 7 and 8 is 111178.
24. Write the greatest 4-digits number of different digits.
Ans. The greatest four different digit are 9, 8, 7 and 6. Thus, required number is the
greatest 4-digit number formed by using the digits 9, 8, 7 and 6, which is 9876.
25. Write the smallest 6-digit number using three different digits.
Ans. The required number is 100002.
26. Write the greatest 6 - digit number using three different digit.
Ans. The greatest three different digits are 9, 8 and 7 Thus, the required number is 999987.
27. Find the difference of the place values of the two 7s in 73810724.
Ans. The place value of 7 at the crores place = 70000000. The place value of 7 at the
hundreds place = 700. Hence, the required difference = 70000000 – 700 = 69999300.
28. Find the sum of the place values of the two 5s in 50050031.
Ans. The place value of 5 at the crores place = 50000000. The place value of 5 at the ten
thousands place = 50000. Hence, the required sum = 50000000 + 50000 = 50050000.
29. Arrange the following numbers in the ascending order 3763214, 18340217, 984671,
3790423, 18431056.
Ans. Let us arrange the given numbers in a place value chart, as shown below
Hence, the given numbers in the ascending are : 984671 < 3763214 < 3790423 <
18340217 < 18431056.
30. What is the true-value of 5 in the numbers ? (i) C T - L L T -Th Th H T O
3
7
3
2
1
4
6
3542 (ii) 5792 (iii) 50231
8
2
1
3
4
0
1
7
Ans. (i) 3542 True-value = 5 (ii) 5792 True-value
9
4
6
7
1
8
= 5 (iii) 50231 True-value = 5
3
4
7
0
2
3
9
31. What is the local value of 2 in the numbers ?
1
8
4
1
0
5
6
3
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(i) 2100
(ii) 2745 (iii) 2003 (iv) 1020
Ans. (i) 2100, the digit 2 is at thousand’s place, so its local value is = 2 × 1000 = 2000.
(ii) 2745, the digit 2 is at thousand’s place, so its local-value is = 2 × 1000 = 2000
(iii) 2003 the digit 2 is at thousand’s place so its local-value is = 2 × 1000 = 2000.
(iv) 1020, the digit 2 is at ten’s place, so its local value is = 2 × 10 = 20.
32. (i) Find the difference between the place-values, of 8 in 1, 84, 536 and 67, 58, 321.
Ans. (i) Place value of 8 in 1, 84,536 = 8 × 10, 000 = 80, 000 and 67, 58, 321 = 8 × 1,
000 = 8,000
Difference in place values = 72,000.
(ii) Find the difference between the place values of 4 in 65,32, 410 and 87, 48, 290.
Place -value 4 in 65,32,410 = 4 × 100 = 400 and 40, 000. ∴ Difference in
place values = 40, 000 – 400 = 39, 600.
33. (i) Find the sum of the place-values of 7 in 3, 72, 574.
Ans. Place values of 7s in 3,72,574 are
Place value of 7 at ten’s place = 7 × 10 = 70.
and 7 at thousand place = 7 × 10, 000 = 70, 000.
∴ Sum of the place values = 70,000 + 70 = 70, 070.
(ii) Find the sum of the place values of 9 in 5, 39, 924.
Ans.
In 5, 39, 924. Place value of 9 at hundred’s place = 9 × 100 = 900.
Place value of 9 at thousand’s place = 9 × 1,000 = 9, 000
∴ Sum of the place values = 9, 000 + 900 = 9, 900.
34. Without making any actual division, find which of the following numbers 9012,
4005, 2010, 504, 111111, 11112, 11121, 99912 are : (i) divisible
by
2.
(ii) divisible by 3. (iii)divisible by 5. (iv) divisible by 10.
Ans. (i) A number is divisible by 2, if its (unit) digit is an even number or zero. So,
9012, 2010, 504, 11112, 99912 are divisible by 2.
(ii) A number is divisible by 3, if the sum of its digits is divisible by 3. Number
divisible by 3 are 9012, 4005, 2010, 504, 111111, 11112, 11121, 99912 as
their sums are 12, 9, 3,9, 6, 6, 6, 30 respectively.
(iii) A number is divisible by 5, if its last (unit) digit is 5 or 0.
From the given numbers only the number divisible by 5 are 4005, 2010.
(iv) A number is divisible by 10, if its unit digit is zero from the above given number only 2010 is divisible by 10.
35.Find the difference between the place value and the face value of the digit 6 in the
Class - VI Mathematics
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Ans.
36.
Ans.
37.
Ans.
number 72601
Place of 6 in 72601 is 600. Face value of 6 in 72601 = 6
∴ The required difference = 600 – 6 = 594.
Write all possible numbers using the digits 7, 0, 6. Repetition of digits is not allowed.
Possible numbers are 0, 6, 7, 76, 67, 70, 60, 706, 607, 760, 670.
Write down the three consecutive numbers succeeding 701259.
701259 + 1 = 701260, 701260 + 1 = 701261, 701261 + 1 = 701262
∴ Numbers are the 701260, 701261, 701262.
Write down the three consecutive numbers preceding 35401.
35401 – 1 = 35400 – 1 = 35399 – 1 = 35398.
Numbers are 35400,35399, 35398.
(i) Determine the difference of the place values of two 7’s in 3701472.
Place values of 7 in 3701472 are 70 and 7000000
38.
Ans.
∴
39.
Ans.
∴ Difference = 7000000 – 6999930
(ii) Find the difference between the place value and the face value of the digit 9 in the
number 229301.
Ans. Place value of 9 229301 is 9000 Face value of 9 in 229301 = 9
∴ Difference = 9000 – 9 = 8991.
(iii) Determine the product of place value and the face value of the digit 4 in the
number 5437.
Ans. Place value of 4 in 5437 = 400. Face value of 4 in 5437 = 4
∴ Product = 400 × 4 = 1600.
40. Evaluate each of the following, using the number line :
(i) ( + 3) + ( + 5)
+3
Ans. ( + 3) + ( + 5) = + 8
–3 –2 –1
+5
0 +1 +2 +3 +4 +5 +6 +7 +8
(ii) ( + 4) + (– 3)
–3
+4
Ans. (+ 4) + ( – 3) = 4 – 3 = + 1
–3 –2 –1
0 +1 +2 +3 +4 +5 +6 +7
(iii) (– 1) + (– 3)
Class - VI Mathematics
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–3
Ans. (– 1) + (– 3) = – 1 – 3 = – 4
–1
–5 –4 –3 –2 –1
(iv) (– 3) – (– 5)
Ans. (– 3) – (–5) = – 3 + 5 = + 2
–3
0 +1 +2 +3 +4 +5
+2
–5 –4 –3 –2 –1
(v) (+ 4) – (– 6)
Ans. (+ 4) – ( – 6) = 4 + 6 = + 10
0 +1 +2 +3 +4 +5
+5
–3
–5 –4 –3 –2 –1
(vi) (+ 6) – (– 3)
Ans. (+ 6) – (– 3) = 6 + 3 = + 9
0 +1 +2 +3 +4
+6
+3
–3 –2 –1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12
(vii) (+ 5) – (+ 3)
Ans. (+ 5) – (+ 3) = 5 – 3 = + 2
+5
–3
–6 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 +6 +7
(viii) (+3) – (+ 5) + (+ 4)
Ans. (+ 3) – (+ 5) + (+ 4) = 3 – 5 + 4 = 7 – 5= + 2
–5
+3
+4
–7 –6 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 +6 +7 +8
41. Represent each of the following fractions on number line :
(i)
Ans.
4
7
4
7
(ii) –
0
1
7
2
7
3
7
4
7
5
7
6
7
1
3
4
Class - VI Mathematics
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Ans. –
–1
3
4
(iii) –
1
6
–
1
6
Ans.
(iv) 1
1
3
1
1
3
(v) 1
3
5
1
3
5
Ans.
Ans.
(vi)
Ams.
–3
4
–2
4
–1
4
1
0
–1 –5 – 4 –3 –2 –1
6 6 6 6 6
0
0
1
1
11 12
3
3
2
0
1
11 1 2
5
5
13 14
5
5
2
0
1
11 1 2
5
5
13 14
5
5
2
8
5
8
3
=1
5
5
42. Represent each of the following decimal numbers on number line :
(i) 0.2
Ans.
0.2
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(ii) 0.5
Ans.
0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
(iii) – 0.4
Ans.
– 0.4
-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
(iv) – 0.8
Ans.
– 0.8
-1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
(v) 1.7
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Ans.
1.7
0
1
1.7
2
(vi) – 1.6
Ans.
– 1.6
– 1.6
–2
–1
43. Evaluate each of the following using number line :
6 1 7
+ = =1
7 7 7
Ans.
(ii)
(iii)
6
7
0
1
7
1
7
4
7
3
7
2
7
5
7
7 3
–
8 8
7 3 4
– =
8 8 8
Ans.
Ans.
6 1
+
7 7
0
(i)
2
8
3
8
4
8
5
8
6
8
7
8
6
9
7
9
1
8 5
–
9 9
8 5 3
– =
9 9 9
(iv) 0.7 + 0.1
8
9
0
1
9
5
9
3
9
2
9
4
9
5
9
0.7
Ans.
1
3
8
7
8
0 1
8
6
7
0.7 + 0.1 = 0.8
8
9
1
0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
(v) 0.7 – 0.3
0.3
0.7
Ans.
0.7 – 0.3 = 0.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
(vi) 0.5 – 0.4
0.4
0.5
Ans.
0.5 – 0.4 = 0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
1 1
+
(vii)
2 5
Class - VI Mathematics
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2
10
5
10
1 1 5 2
7
+ = + +=
2 5 10 10
10
Ans.
0
1 2 3 4 5 6 7 8 9 1
10 10 10 10 10 10 10 10 10
44. (i) Draw a number line to represent fractions ;
–1
1 –2
5 5
4
5
2
2
4 2
1
, 2 ; –1 and – .
5
5 5
5
2
5
–5 –4 –3 –2 –1 0 1 2 3 4 5
(ii) Represent the following fractions on the same number line :
(a)
3
4
(b)
7
4
–2
(c)
1
(d)
4
–
3
4
1
–2 – 3 3 7
4 4 4 4
Ans.
–4 –3 –2 –1 0 1 2 3 4
(iii) Represent the following fractions on the same number line:
(a) 0.2
(b)
2.2 (c)
– 1.2 (d)
– 3.2
–3.2
–1.2
0.2
2.2
Ans.
–5 –4 –3 –2 –1
0
1
2
3
4
5
3
and B = 3.5 are two points on the same number line : use the number line
2
to find the distance between A and B.
45. If A = –
–1.5
3.5
A
B
–4 –3 –2 –1 0 1 2 3 4 5
∴ Distance between A and B = (3.5) – (– 1.5) = (3.5 + 1.5) = 5
3
Ans. A = – = –1.5, B = 3.5
2
3
are two points on the same number line ; use the number line
4
to find the distance between P and Q.
46. If P = 2.25 and Q = –
– 0.75
3
Ans. P = 2.25, Q = – = – 0.75
4
Q
2.25
P
–4 –3 –2 –1 0 1 2 3 4
∴ Distance between P and Q = (+2.25) – (– 0.75) = + 2.25 + 0.75 = 3
Class - VI Mathematics
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