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Question 1.
Round off each of the following numbers to their nearest tens:
(i) 77
(ii) 903
(iii) 70 1205
(iv) 999
Solution:
(i) 77
The digit at unit place is 7, which is greater than 5.
Hence, the rounded off number to nearest tens = 80.
(ii) 903
The digit at unit place is 3, which is less than 5.
Hence, the rounded off number to nearest tens = 900.
(iii) 1205
The digit at unit place is 5, which is equal to 5.
Hence, the rounded off number to nearest tens = 1210
(iv) 999
The digit at unit place is 9, which is greater than 5.
Hence, the rounded off number to nearest tens = 1000.
Question 2.
Estimate each of the following numbers to their nearest hundreds:
(i) 1246
(ii) 32057
(iii) 53961
(iv) 555555
Solution:
(i) 1246
The digit at tens place is 4, which is less than 5.
Hence, the rounded off number to nearest hundreds = 1200.
(ii) 32057
The digit at tens place is 5, which is equal to 5.
Hence, the rounded off number to nearest hundreds = 32100.
(iii) 53961
The digit at tens place is 6, which is greater than 5.
Hence, the rounded off number to nearest hundreds = 54000.
(iv) 555555
The digit at tens place is 5, which is equal to 5.
Hence, the rounded off number to nearest hundreds = 555600.
Question 3.
Estimate each of the following numbers to their nearest thousands:
(i) 5706
(ii) 378
(iii) 47,599
(iv) 1,09,736
Solution:
(i) 5706
The digit at hundred place is 7, which is greater than 5.
Hence, the rounded off number to nearest thounsands = 6000.
(ii) 378
The digit at hundred place is 3, which is less than 5.
Hence, the rounded off number to nearest thousands = 0.
(iii) 47,599
The digit at hundred place is 5, which is equal to 5.
Hence, the rounded off number to nearest thousands = 48000.
(iv) 1,09,736
The digit at hundred place is 7, which is greater than 5.
Hence, the rounded off number to nearest thousands = 1,10,000.
Question 4.
Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
(i) 439 + 334 + 4317
(ii) 8325 – 491
(iii) 1,08,734-47,599
(iv) 4,89,348 – 48,365
Solution:
(i) Rounding off to nearest hundreds 439 + 334 + 4317
= 400 + 300 + 4300 = 5000 Rounding off to nearest tens 439 + 334 + 4317
= 440 + 330 + 4320 = 5090
(ii) Rounding off to nearest hundreds 8325 – 491
= 8300 – 500 = 7800 Rounding off to nearest tens 8325 – 491
= 8330 – 490 = 7840
(iii) 1,08,734 – 47,599
Rounding off to nearest hundreds 1,08,734 – 47,599
= 1,08,700 – 47,600 = 61,100 Rounding off to nearest tens 1,08,734 – 47,599
= 1,08,730 – 47,600 = 61,130
(iv) 4,89,348 – 48,365
Rounding off to nearest hundreds 4,89,348 – 48,365
= 4,89,300 – 48,400 = 4,40,900 Rounding off to nearest tens 4,89,348 – 48,365
= 4,89,350 – 48,370 = 4,40,980
Question 5.
Estimate each of the following by rounding off each number nearest to its greatest place:
(i) 730 + 998
(ii) 5,290 + 17,986
(iii) 796-314
(iv) 28,292 – 21,496
Solution:
(i) 730 + 998
Rounding off 730 to its greatest place i.e. hundred place = 700
Rounding off 998 to its greatest place i.e. hundreds place = 1000
Hence, estimated sum = 700 + 1000 = 1700
(ii) 5,290 + 17,986
Rounding off 5,290 to its greatest place i.e. thousands place = 5000
Rounding off 17,986 to its greatest place i. e. thousands place = 18,000 Hence, estimated sum = 5,000 + 18,000 = 23,000
(iii) 796 – 314
Rounding off 796 to its greatest place i.e. hundreds place = 800 Rounding off 314 to its greatest place i.e. hundreds place = 300 Hence, estimated difference = 800 – 300 = 500
(iv) 28,292 – 21,496
Rounding off28,292 to its greatest place i.e. thousands place = 28,000 Rounding off 21,496 to its greatest place i. e. thousands place = 21,000 Hence, estimated difference = 28,000 – 21,000 = 7,000
Question 6.
Estimate the following products by rounding off each of its factors nearest to its greatest place:
(i) 578 × 161
(ii) 9650 × 27
Solution:
(i) 578 × 161
Rounding off 578 to its greatest place i.e. hundreds place = 600
Rounding off 161 to its greatest place i.e. hundreds place = 200
Hence, estimated product = 600 x 200 = 1,20,000
(ii) 9650 × 27
Rounding off 9650 to its greatest place i.e. thousands place = 10000
Rounding off 27 to its greatest place i.e. tens place = 30
Hence, estimated product = 10000 × 30 = 3,00,000
Question 7.
Estimate the following products by rounding off each of its factors nearest to its hundreds place:
(i) 5281 × 3491
(ii) 1387 × 888
Solution:
(i) 5281 x 3491
Rounding off 5281 to its hundreds place = 5300
Rounding off 3491 to its hundreds = 3500
Hence, estimated product = 5300 × 3500 = 1,85,50,000
(ii) 1387 × 888
Rounding off 1387 to its hundreds place = 1400
Rounding off 888 to its hundreds place = 900
Hence, estimated product = 1400 × 900 = 12,60,000
ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 1 Knowing Our Numbers Objective Type Questions
Mental Maths
Question 1.
Fill in the blanks:
(i) The digit …………… has the highest place value in the number 2309.
(ii) The digit …………… has the highest face value in the number 2039.
(iii) The digit …………… has the lowest place value in the number 2039.
(iv) Both Indian and International systems of numeration have …………… period in common.
(v) In the International system of numeration, commas are placed from …………… after every …………… digits.
(vi) The bigger number from the numbers 57,631 and 57,361 is ……………
(vii) 1 crore = …………… million
(viii)The smallest 4-digit number with 3 different digits is ……………
(ix) The greatest 4-digit number with 3 different digits is ……………
(x) 15 km 300 m = …………… m
(xi) 7850 cm = …………… m …………… cm
(xii) The number 5079 when estimated to the nearest hundreds is ……………
Solution:
(i) The digit 2 has the highest place value in the number 2309.
(ii) The digit 9 has the highest face value in the number 2039.
(iii) The digit 0 has the lowest place value in the number 2039.
(iv) Both Indian and International systems of numeration have ones period in common.
(v) In the International system of numeration, commas are placed from right after every 3 digits.
(vi) The bigger number from the numbers 57,631 and 57,361 is 57,631.
(vii) 1 crore = 10 million (viii)The smallest 4-digit number with 3 different digits is 1002.
(ix) The greatest 4-digit number with 3 different digits is 9987.
(x) 15 km 300 m = 15300 m
(xi) 7850 cm = 78 m 50 cm
(xii) The number 5079 when estimated to the nearest hundreds is 5100.
Question 2.
State whether the following statements are true (T) or false (F):
(i) The difference between the place value and the face of the digit 7 in the number 2701 is 693.
(ii) The smallest 4-digit number -1 = the greatest 3-digit number.
(iii) The place of a digit is independent of whether the number is written in the Indian system or International system of numeration.
(iv) In the International system, a number having less number of digits is always smaller than the number having more number of digits.
(v) The estimated value of 9999 to the nearest tens is 10000.
Solution:
(i) The difference between the place value and the face of the digit 7 in the number 2701 is 693. True
(ii) The smallest 4-digit number-1 = the greatest 3-digit number. True
(iii) The place of a digit is independent of whether the number is written in the Indian system or International system of numeration.
True
(iv) In the International system, a number having less number of digits is always smaller than the number having more number of digits.
True
(v) The estimated value of 9999 to the nearest
Question 2.
State whether the following statements are true (T) or false (F):
(i) The difference between the place value and the face of the digit 7 in the number 2701 is 693.
(ii) The smallest 4-digit number -1 = the greatest 3-digit number.
(iii) The place of a digit is independent of whether the number is written in the Indian system or International system of numeration.
(iv) In the International system, a number having less number of digits is always smaller than the number having more number of digits.
(v) The estimated value of 9999 to the nearest tens is 10000.
Solution:
(i) The difference between the place value and the face of the digit 7 in the number 2701 is 693. True
(ii) The smallest 4-digit number-1 = the greatest 3-digit number. True
(iii) The place of a digit is independent of whether the number is written in the Indian system or International system of numeration.
True
(iv) In the International system, a number having less number of digits is always smaller than the number having more number of digits.
True
(v) The estimated value of 9999 to the nearest
Multiple Choice Questions
Choose the correct answer from the given four options (3 to 17):
Question 3.
The face value of the digit 5 in the number 36503 is
(a) 5
(b) 503
(c) 500
(d) none of these
Solution:
The place value of 5 at hundred’s place
= 5 × 100 = 500 (c)
Question 4.
The difference between the place values of 6 and 3 in 76834 is
(a) 3
(b) 5700
(c) 5930
(d) 5970
Solution:
The place value of 6 at thousand’s place
= 6 × 1000 = 6,000
The place value of 3 at ten’s place
= 3 × 10 = 30
The difference between the place value of 6 and 3 = 6000 – 30 = 5970 (d)
Question 5.
The sum of the place values of all the digits in 5003 is
(a) 8
(b) 53
(c) 5003
(d) 8000
Solution:
The place value of 3 at one’s place
=3 × 1 = 3
The place value of 0 at ten’s place = 0 × 10 = 0
The place value of 0 at hundred’s place = 0 × 100 = 0
The place value of 5 at thousand’s place = 5 × 1000 = 5000
The sum of the place value of all the digits
in 5003 = 3 + 0 + 0 + 5000 = 5003 (c)
Question 6.
The total number of 4-digit numbers is
(a) 9000
(b) 9999
(c) 10000
(d) none of these
Solution:
The greatest 3-digit number = 999 The greatest 4-digit number = 9999 .’. The total number of 4-digit numbers
= 9999 – 999 = 9000 (a)
Question 7.
The product of the place values of two-threes in 73532 is
(a) 9000
(b) 90000
(c) 99000
(d) 1000
Solution:
The place value of 3 at ten’s place = 3 × 10 = 30
The place value of 3 at thousand’s place = 3 × 1000 = 3000
The product of place value of two threes = 30 × 3000 = 90000 (b)
Question 8.
The smallest 4-digit number having distinct digits is
(a) 1234
(b) 1023
(c) 1002
(d) 3210
Solution:
The smallest 4-digit number having distinct digits is 1002. (c)
Question 9.
The largest 4-digit number having distinct digits is
(a) 9999
(b) 9867
(c) 9786
(d) 9876
Solution:
The largest 4-digit number having distinct digits is 9867. (b)
Question 10.
The largest 4-digit number is
(a) 9999
(b) 9876
(c) 9990
(d) none of these
Solution:
The largest 4-digit number is 9999. (a)
Question 11.
The difference between the largest number of 3-digit and the largest number of 3-digit with distinct digits is
(a) 0
(b) 10
(c) 12
(d) 14
Solution:
The largest number of 3-digit = 999
The largest number of 3-digit with distinct digits = 987
∴ Their difference = 999 – 987 = 12 (c)
Question 12.
If we write natural numbers from 1 to 100, the number of times the digit 5 has been written is
(a) 11
(b) 15
(c) 19
(d) 20
Solution:
If we write natural numbers from 1 to 100, the number of times the digit 5 has been written is 20. (d)
Question 13.
The number 28,549 when rounded off to the nearest hundreds is
(a) 28,000
(b) 28,500
(c) 28,600
(d) 29,000
Solution:
28,549
The digit at tens place is 4, which is less than 5.
Hence, the rounded off number to nearest hundreds = 28,500. (b)
Question 14.
The smallest natural number which when rounded off to the nearest hundreds as 500 is
(a) 499
(b) 501
(c) 450
(d) 549
Solution:
The smallest natural number which when rounded off to the nearest hundreds as 500 is 450. (c)
This is so because the digit at tens place is 5, which is equal to 5.
Question 15.
The greatest natural number which when rounded off to the nearest hundreds as 500 is
(a) 549
(b) 599
(c) 450
(d) none of these
Solution:
The greatest natural number which when rounded off to the nearest hundreds as 500 is 549. (a)
This is so because the digit at tens place is 4, which is less than 5.
Question 16.
The greatest 5-digit number formed by the digits 3, 0, 7 is
(a) 33077
(b) 77730
(c) 77330
(d) none of these
Solution:
The greatest 5-digit number formed by the digits 3, 0, 7 is 77730. (b)
Question 17.
In the International place value system, we write 1 billion for
(a) 10 lakh
(b) 1 crore
(c) 10 crore
(d) 100 crore
Solution:
In the International place value system, we write 1 billion for 100 crore. (d)
Value Based Questions
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Question 1.
The distance between Anu’s home and her school is 4 km 850 m. Everyday she cycles both ways. Find the distance covered by her in a week. (Sunday being a holiday).
What are the advantages of cycling?
Solution:
Distance between Anu’s home and her school = 4 km 850 m = 4 x 1000+ 850 = 4850 m Distance travelled by Anu per day = 4850 m x 2 = 9700 m Since, in a week there are 7 days but Sunday is off.
Hence, distance travelled by Anu for 6 days (a week) = 9700 × 6 = 58200 m
= 58 km 200 m
Cycling is good for health and it saves fuel and helps in reducing pollution.
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Higher Order Thinking Skills (HOTS)
Question 1.
Is there any digit whose place value is always equal to its face value irrespective of its position in any number?
Solution:
Yes, the digit is 0.
Question 2.
Write all 4-digit numbers that can be formed with the digits2 and 5, using both digits equal number of time. Also find their sum.
Solution:
Possible numbers are : 2255, 2552, 2525, 5225, 5252, 5522
and their sum = 2255 + 2552 + 2525 + 5225 + 5252 + 5522 = 23331
Thousand Hundred Tens Ones
2 2 5 5
2 5 5 2
2 5 2 5
5 2 2 5
5 2 5 2
5 5 2 2
Question 3.
What is the difference between the smallest 6-digit number with five different digits and the greatest 5-digit number with four different digits?
Solution:
The smallest 6-digit number with five different digits = 100234.
The greatest 5-digit number with four different digits = 99876.
Their difference = 100234 – 99876 = 358
Question 4.
How many times does the digit 3 occur at tert’s place in natural numbers from 100 to 1000?
Solution:
90 times i.e. 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 and upto 983, 993
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ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 1 Knowing Our Numbers
Question 1.
Write the numeral for each of the following numbers and insert commas correctly:
(i) Six crore nine lakh forty seven.
(ii) One hundred four million seven hundred twenty two thousand three hundred ninety four.
Solution:
(i) 6,09,00,047
(ii) 104,722,394
Question 2.
Insert commas suitably and write the numebr 30189301 in words in Indian and International system of numeration.
Solution:
International system : 30,189,301
Three crore one lakh eighty nine thousand three hundred one Thirty million one hundred eighty nine thousand three hundred one
Question 3.
Find the difference between the place value and the face value of the digit 6 in the number 72601.
Solution:
Place value of 6
Question 4.
Write all possible two-digit number using the digits 4 and 0. repetition of digits is allowed.
Solution:
Possible digit numbers = 40, 44
Question 5.
Write all possible natural numbers using the digits 7, 0, 6. Repetition of digits is not allowed.
Solution:
The given digits are 7,0, 6 and repetition of digits is not allowed.
The one- digit numbers that can be formed are 7 and 6.
We are required to write 2-digit numbers.
Out of the given digits, the possible ways of choosing the two digits are
7, 0; 6, 0; 6, 7
Using the digits 7 and 0, the numbers are 70.
Similarily, Using the digits 6 and 0, the numbers are 60
Using the digits 6 and 7, the numbers are 67 and 76.
Hence, all possible 2-digit numbers are
60, 70, 67, 76
Now, We are required to write 3-digit numbers using the digits 7, 0, 6 and the repetition of the digits is not allowed. Keeping 0 at unit’s place, 3-digit number obtained are 670 and 760.
Keeping 6 at unit’s place, 3-digit number obtained are 706.
Keeping 7 at unit’s place, 3-digit number obtained are 607.
Hence, all possible 3-digit numbers are : 670, 760, 706 and 607.
All possible numbers using the digits 7, 0 and 6 are
6, 7, 76, 67, 70, 60, 706, 607, 760, 670.
Question 6.
Arrange the following numbers in ascending order:
3706, 58019, 3760, 59801, 560023
Solution:
3706, 3760, 58019, 59801, 560023
Question 7.
Write the greatest six-digit number using four different digits.
Solution:
Greatest six-digits number using four different digit is 999876.
Question 8.
Write the smallest eight-digit number using four different digits.
Solution:
Smallest eight-digit number = 10000023
Question 9.
Find the difference between the greatest and the smallest 4-digit numbers formed by the digits 0, 3, 6, 9.
Solution:
The greatest 4-digit number using 0, 3, 6, 9 = 9630
The smallest 4-digit number using 0, 3, 6, 9 = 3069
∴ Their Difference = 9630 – 3069 = 6561
Question 10.
Find the sum of the four-digit greatest number and the five-digit smallest number, each number having three different digits.
Solution:
Four digit greatest number with three different digits = 9987
Five digit smallest number with three different digit = 10002
∴ Their Sum = 9987 + 10002 = 19989
Question 11.
Write the greatest and the smallest four-digit numbers using four different digits with the conditions as given:
(i) Digit 3 always at hundred’s place.
(ii) Digit 0 always at ten’s place.
Solution:
(i) 9387; 1302
(ii)9807; 1203
Question 12.
A mobile number consists of ten digits. First four digits are 9, 9, 7 and 9. Make the smallest mobile number by using only one digit twice from the digits 8, 3, 5, 0, 6.
Solution:
The mobile number is 9979003568.
Question 13.
Two stitch a uniform, 1 m 75 cm cloth is needed. Out of 153 m cloth, how many uniforms can be stitched and how much cloth will remain?
Solution:
Total cloth 153 m = 15300 cm
To stich a uniform, cloth needed
= 1 m 75 cm = 175 cm
Total uniforms can be stiched =
Hence, 87 uniforms can be stiched 75 cm cloth will remain extra.
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