ICSE Class 6 Math: Chapter 1 – Knowing Our Numbers

ML Agarwal Solutions

 

Exercise 1.1

1. Write the smallest natural number. Can you write the largest natural number?  

Solution:  

The smallest natural number is 1.  

We cannot write the largest natural number because it is infinite.  

2. Fill in the blanks :  

(i) 1 lakh = ….. ten thousand  

(ii) 1 million = ……hundred thousand  

(iii) 1 crore = …… ten lakh  

(iv) 1 billion = …… hundred million  

Solution:  

(i) 1 lakh = 10 ten thousand  

(ii) 1 million = 10 hundred thousand  

(iii) 1 crore = 10 ten lakh  

(iv) 1 billion = 10 hundred million  

3. Insert commas suitably and write each of the following numbers in  words in the indian system and the international system of  numeration.  

(i) 506723  

(ii) 180018018  

Solution:  

Indian system  

(i) 506723 = 5,06,723  

Five lakh six thousand seven hundred and twenty three.  

(ii) 180018018 = 18,00,18,018  

Eighteen crore eighteen thousand and eighteen.  

International system  

(i) 506723 = 5,06,723  

fiven hundred six thousand seven hundred and twenty three.  

(ii) 180018018 = 18,00,18,018  

one hundred eighty million eithteen thousand and eighteen. 

4. Write the following numbers in expanded form:  (i) 750687  

(ii) 5032109  

Solution:  

Given numbers can be written in expanded form as,  (i) 750687 = 700000 + 50000 + 600 + 80 + 7  

(ii) 5032109 = 5000000 + 30000 + 2000 + 100 + 9  

5. Write the following numbers in Figures :  

(i) Seven lakh three thousand four hundred twenty.  

(ii) Eighty crore twenty three thousand ninety three.  

Also write the above numbers in the place value chart. 

Solution:  

(i) 7,03,420  

(ii) 80,00,23,093  

By using place value chart, 

6. Write each of the following numbers in numeral form and place  commas correctly:  

(i) Seventy three lakh seventy five thousand three hundred seven.  (ii) Nine crore five lakh forty one.  

(iii) Fifty eight million four hundred twenty three thousand two hundred   two.  

Solution:  

(i) 73, 75,307  

(ii) 9,05,00,041  

(iii) 58, 423,202  

7. Write the face value and place value of the digit 6 in the number  756032.  

Solution:  

756032  

Face value of 6 = 6  

Place value = 6000 

8. Find the difference between the place value and the face value of  the digit 9 in the number 229301.  

Solution :  

Place value of 9   in   229301  is  9000  

 Face value of 9  in  229301   is  9  

difference = 9000   – 9  

 = 8 9 91  

Question 9: Determine the difference of the place value of two 7’s in  37014472 and write it in words in International system.  

Solution :  

The given number in International system can be written as 37,014,472 

 The place value of 7 at ten’s place = 7 × 10 = 70 

The place value of 7 at 7 million’s place = 7 × 1,000,000 = 7,000,000 

 The required difference = 7,000,000 – 70 = 6,999,930  

Six million nine hundred ninty thousand nine hundred thirty. 

Question 10.  

Determine the product of place value and the face value of the digit 4 in  the number 5437.  

Solution:  

Place value of 4  in 5437   is  400  

Face value of 4  in 5437   is  4  

Product = 400 × 4 = 1600 

Question 11.  

Find the difference between the number 895 and that obtained on  reversing its digits.  

Solution :  

First number = 895  

Reversed number = 598  

difference = 297 

 

Exercise 1.2  

Question 1.  

Use the appropriate symbol < or > to fill in the blanks :  (i) 173 …… 189  

(ii) 1058 …….. 1074  

(iii) 8315 ……8037  

Solution:  

(i) 173 < 189    

(ii) 1058 <  1074                                                                                                                                

(iii) 8315 > 8037  

Question 2 :  

In each of the following pairs of numbers, state which number is  smaller:  

(i) 553,503  

(ii) 41338,1139  

(iii) 25431,24531  

Solution:  

(i) 503 number is smaller.  

(ii) 1139 number is smaller.  

(iii) 24531 number is smaller.  

Question 3 : Find the greatest and the smallest numbers in each row  :  

(i) 71834, 75284, 571, 2333, 594  

(ii) 9853, 7691, 9999, 12002.  

Solution:  

(i) 571 is the smallest number and 75284 is the greatest number. 

(ii) 7691 is the smallest number and 12002 is the greatest number.  

Question 4 :  

Arrange the following numbers in ascending order:  

304, 340, 34, 43, 430  

Solution:  

Arranging the following numbers in ascending order.  

34, 43, 304, 340, 430  

Question 5 :  

Arrange the following numbers in descending order :  

53, 7333, 553, 7529, 335.  

Solution :  

Arranging the following numbers in Descending order :  7529, 7333, 553, 335, 53 

Question 6.  

Write all possible 2-digits numbers that can be formed by using the  digits, 3 and 4. Repetition of digits is not allowed. Also find their SUM

solution :  

The given digits are 2, 3, 4 and repetition of digits is not allowed.  

Out of the given digits, the possible ways of choosing the two digits are  2, 3; 2, 4; 3, 4  

Using the digits 2 and 3, the numbers are 23 and 32  

Similarly, Using the digits 2 and 4, the numbers are 24 and 42

  Using the digits 3 and 4, the numbers are 34 and 43  

Hence, all possible 2-digit numbers are 23, 32, 24, 42, 34, 43

  ∴ Sum of above numbers  

= 23 + 34 + 32 + 24 + 43 + 42 = 198.  

Question 7 :  

Write all possible 3-digits numbers using the digits 3,1 and 5.  Repetition of digits is not allowed.  

Solution :  

We are required to write 3-digit numbers using the digits 1, 3, 5 and the  repetition of the digits is not allowed.  

Keeping 1 at unit’s place, 3-digit number obtained are 351 and 531.  Keeping 3 at unit’s place, 3-digit number obtained are153 and 513.  Keeping 5 at unit’s place, 3-digit number obtained are 315 and 135. 

Hence, all possible 3-digit numbers are : 315, 351, 153, 135, 531, 513  

Question 8:  

Write all possible 3-digits numbers using the digits 7, 0 and 6.  Repetition of digits is not allowed. Also, find their sum. 

Solution:  

we are required to write 3 –digit numbers using the digits 0,6,7 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. 

 Keeping 7 at unit’s place, 3- digit number obtained are 607.  

Hence, all possible 3- digit numbers are : 670, 760, 607, 706.  

∴ Sum of above numbers  

= 670 + 760 + 607 + 706 = 2743  

Question : 9  

Write all possible 2- digit numbers using the digits 4, 0 and 9. Repetition  of digits is not allowed . Also find their sum.  

Solution:  

The given digits are 0, 4, 9 and repetition of digits is not allowed.  

Out of the given digits, the possible ways of choosing the two digits are  4, 0; 4, 9; 9, 0  

Using the digits 4 and 0, the number are 40. 

Similarly, Using the digits 4 and 9, the numbers are 49 and 94.  

Using the digits Hence, all possible 2-digit numbers are 40, 49, 90, 94

  ∴ Sum of above numbers = 40 + 49 + 90 + 94 = 273  

Question 10 : Write all possible 2-digit numbers that can be formed by  using the digit 3, 7 and 9. Repetition of digits is allowed.  

Solution:  

The given digits are 3, 7, 9 and repetition of digits is not allowed. Out of  the given digits, the possible ways of choosing the two digits are 3, 7; 3,  9; 7, 9  

Using the digits 3 and 7, the numbers are  37, 73, 33 and 77.  

Similarly, Using the digits 3 and 9, the numbers are 39, 93, and 99.  

Using the digits 7 and 9, the numbers are 79 and 97.  

Hence, all possible 2-digit numbers are  

37, 73, 33, 77, 39, 93, 99, 79, 97  

Question 11.  

Write all possible numbers using the digits 3, 1 and 5. Repetition of  digits is not allowed.  

Solution:  

The given digits are 1,3, 5 and repetition of digits is not allowed.  The one-digit numbers that can be formed are 1, 3 and 5.  We are required to write 2-digit numbers. 

Out of the given digits, the possible ways of choosing the two digits are  1, 3, 1, 5, 3, 5  

Using the digits 1 and 3, the numbers are13 and 31.  

Similarly, Using the digits 1 and 5, the numbers are 15 and 51.  Using the digits 3 and 5, the numbers are 35 and 53.  

Hence, all possible 2-digit numbers are  13, 31, 15, 51, 35, 53  

Now, We are required to write 3-digit numbers using the digits 1, 3, 5  and the  repetition of the digits is not allowed. Keeping 1 at unit’s place, 3-digit  number obtained are 351 and 531.  

Keeping 3 at unit’s place, 3-digit number obtained are 153 and 513.  Keeping 5 at unit’s place, 3-digit number obtained are 315 and 135. 

 Hence, all possible 3-digit numbers are : 315, 351, 153, 135, 531, 513  All possible numbers using the digits 3, 1 and 5 are :  

1, 3, 5, 31, 13, 35, 53, 15, 51, 315, 153, 351, 531, 513, 135.  

Question 12.  

How many 6-digit numbers are there in all ?  

Solution:  

The greatest 6- digit numbers = 999999  

The greatest 5-digit numbers = 99999  

The total number of 6-digit numbers  

= 999999 – 99999 

= 900000  

Question 13. Write down the greatest number and the smallest number  of 4-digits that can be formed by the digits 7,5, 0 and 4 using each digit  only once.  

Solution:  

We are required to write 4-digits numbers using the digits 7, 5, 0, 4 and  the repetition of the digits is not allowed.  

Keeping 0 at unit’s place, 4 – digit number obtained are 4570, 4750,  5470, 5740, 7540, and 7540.  

Keeping 4 at unit’s place, 4-digit number obtained are 5074, 5704, 7054  and 7504. Keeping 5 at unit’s place, 4-digit number obtained are  

Keeping 7 at unit’s place, 4-digit number obtained are 4057, 4507, 5047  and 5407.  

Hence, all possible 4-digit numbers are L 4570, 4750, 5470, 5740, 7450,  7540, 5074, 5704, 7054, 7504, 4075, 4705, 7045, 7405, 4057, 4507,  5047, 5407  

Hence, The Greatest number = 7540 and the smallest number = 4057  

Question 14 : Rearrange the digits of the number 5701024 to get the  largest number and the smallest number of 7 digits.  

Solution:  

Largest number = 7542100  

[Method used : Firstly, write largest to smallest number in descending  order.] Smallest number = 1002457. 

[Method used : Firstly, write smallest to largest number in ascending  order. ( start from 1 then 0 then next digits)]  

Question 15.  

Keeping the place value of digits 3 in the number 730265 same,  rearrange the digits of the given number to get the largest number and  smallest number of 6 digits.  

Solution:  

Keeping the same place values of digit 3 in the number 730265 and  rearranging the digits of the given number,  

Greatest number of 6 digits= 736520 Smallest number of 6 digits =  230567.  

Question 16.  

From the smallest and greatest 4-digit numbers by using any one  digit twice from the digits :  

(i) 5, 2, 3, 9  

(ii) 6, 0, 1, 4  

(iii) 4, 6, 1, 5, 8  

Solution:  

(i) The smallest 4-digit numbers = 2235  

and the greatest 4-digit numbers = 9935  

(ii) The smallest 4-digit numbers = 1004  

The greatest 4-digit numbers = 6641 

(iii) The smallest 4-digit numbers = 1145  

The greatest 4-digit numbers = 8865  

Question 17.  

Write  

(i) the greatest number of 6 digits  

(ii) the smallest number of 7 digits. Also find their difference.  Solution:  

(i) Greatest 6 digit number = 999999  

(ii) Smallest 7 digit number = 1000000  

∴ Their Difference 1000000  – 999999  = 1  

Question 18.  

Write the greatest 4-digit number of distinct digits. 

  Solution:  

Greatest 4-digit number of four different digit = 9876  

Question 19.  

Write the smallest 4-digit number of distinct digits. 

  Solution:  

Smallest 4-digit number of four digit = 1023 

Question 20.  

Write the greatest 6-digit number using three different digits. 

  Solution:  

Greatest 6 digit number using three different digits = 999987.  

Question 21.  

Write the smallest 7-digit number using four different digits. 

 Solution:  

Smallest 7 digit number by using four different digit = 1000023  

Question 22.  

Write the greatest and the smallest 4-digit numbers using four different  digits with the conditions as given :  

(i) Digit 7 is always at units place.  

(ii) Digit 4 is always at tens place.  

(iii) Digit 9 is always at hundreds place.  

(iv) Digit 2 is always at thousands place.  

Solution:  

(i) 9867; 1027  

(ii) 9847; 1042  

(iii) 8976; 1902  

(iv) 2987; 2013 

 

Exercise 1.3  

Question 1.  

In a particular year, a company manufactured 8570435 bicycles and next  year it manufactured 8756430 bicycles. In Which year more bicycles  were manufactured and by how many ?  

Solution:  

Production of bicycles in a particular year  = 85,70,435  

Production of bicycles in a next year  = 87,56,430  

Both the numbers 85,70,435 and 87,56,430 are 7 digit numbers and 87  > 85.  

∴ 87, 56,430 > 85,70, 435  

∴ Their Difference  

 8756430  – 8570435  = 185995  

Hence, the production of bicycles in a next year is more and by  1,85,995 cycles of 87,56,430. 

Question 2. What number must be subtracted from 1,02,59,756 to get  77,63,835 ?  

Solution:  

First number = 1,02,59,756  

Resultant number = 77,63,835  

 1,02,59,756  – 77,63,835  = 2495921  

The number to be subtracted from first number to obtain the resultant  number is 24,95,921.  

Question 3.  

The sale receipt of a company during a year was ₹ 30587850. Next year  it increased by ₹6375490. What was the total sale receipt of the  company during these two years ?  

Solution: 

Sale in the first year = ₹30587850  

Sale increased in the next year by = ₹6375490 

∴ Sale in the second year  

= ₹ 30587850 + ₹ 6375490 

= ₹ 36963340  

Sale in the first year + Sale in the second year

 30587850  + 36963340  = 67551190 

Total sale for the two years = ₹67551190 

Question 4.  

A machine manufactures 23875 screws per day. How many screws did it  produce if the year 2012 ? Assume that the machine worked on all the  days of the year ?  

Solution:  

Production of screws per day = 23875  

2012 is a leap year, So there are 366 days  

Total production of screws per year  

= 23875 × 366 = 8738250  

 Ans  8738250 

Question:5  

A merchant had ₹ 78,592 with him. He placed an order for puchasing  54 bicycles at ₹ 970 each. How much money will remain with him after  the purchase ?  

Solution :  

Total money available with merchant = ₹ 78,592  

Total money paid for purchasing 54 bicycles at ₹ 970 = ₹52,380 

 Money left with merchant  

= ₹ 78,592 – ₹52,380  

= ₹26,212

Question 6.  

Amitabh is 1m 82 cm tall and his wife is 35 cm shorter than him. What  is his wife’s height ?  

Solution:  

Height of Amitabh = 1m 82 cm  

= 1 × 100 + 82   = 182 cm  

Amitabh wifes 35 shorter than Amitabh  

∴ Amitabh wife height = 182 – 35 = 147 cm  

Question 7.  

The mass of each gas cylinder is 21kg 270g. What is total mass of 28  such cylinders ?  

Solution:  

Mass of one gas cylinder = 21 kg 270g  

= 21 × 1000 + 270 g  

= 21270 g  

Total mass of 28 gas cylinder = 21270 × 28  

= 595560g  

= 59kg 556g  

21278  

× 28  

170160  

42450× 

595560 

Question 8.  

In order to make a shirt, 2m 25 cm Cloth is needed. What length of cloth  is required to make 18 such shirts ?  

Solution :  

The length of cloth required to stitch one shirt = 2m 25 cm  = 2 × 100 + 25   = 225    

The length of cloth required to stitch 18 shirts  

= 225 × 18 = 4050    

= 40 m 50cm  

Question 9:  

The total mass of 12 packets of sweets, each of the same size, is 15 kg  600g. What is the mass of each such packet ?  

Solution:  

Total mass of 12 packets of sweets  

= 15kg 600g  

= 15 × 1000 + 600  

= 15600 g  

Total mass of one packet of sweets  

= 15600 – 12 = 1300g  

= 1 kg 300g 

 1300  

 12 15600  

– 12  

 36  

 -36  

 0  

Question 10.  

A vessel has 4 litres 500 millilitres of orange juice. In how many  glasses, each of 25 mL capacity, can it be filled ?  

Solution :  

Total capacity of vessel containing orange juice = 4 litres 500 mL  = 4 × 1000 + 500mL  

= 4500 mL  

Size of glass = 25mL  

Number of glass =                

     ! ”  ## 

= ^$%&& 

‘% 

= 180 glasses 

 180  

 25 4500  

 25  

 200  

 200  

 0  

Question 11.  

To stitcha trouser, 1m 30 cm cloth is needed. Out of 25m cloth, how  many trousers can be stitched and how much cloth will remain ?  

Solution :  

Total length of cloth available = 25m  

= 25 × 100 = 2500 cm  

The length of cloth required to stitch a trouser  

= 1m 30cm  

= 100 + 30cm = 130cm  

Dividing 2500 by 130, we get quotient = 19 and remainder = 30 

 19  

 130 2500  

 130  

 1200  

 1170  

 30  

∴ The number of trousers that can be stitched = 19  and the length of the remaining cloth = 30 cm 

Exercise 1.4  

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 7, which is greater than 5.  

Hence, the rounded off number to nearest tens = 80.  

(iii) 1205  

The digit at unit place is 5, which is greater than 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 nearst 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 thousands = 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 = 7840  

(iii) 1,08,734 – 47,599  

Rounding off to nearest hundreds 1,08,734 -47,599  

= 1,08,734 – 47,599  

= 61,130 

(iv) 4,89,348 – 48 , 365  

Rounding off to nearest hundreds 4,89,348 – 48 , 365  = 4,89,348 – 48 , 365  

= 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. hundred place = 1000  Hence, estimated sum = 700 + 1000 = 1700  

(ii) 5,290 + 17,986  

Rounding off 5,290 to its greatest place i.e. hundred place = 5000  Rounding off 17,986 to its greatest place i.e. hundred place = 18,000 

Hence, estimated sum = 5000 + 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. hundred place = 300  Hence, estimated difference = 800 – 300 = 500  

(iv) 28,292 – 21,496  

Rounding off 28,292 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, estimates product = 600 × 200 = 1,20,000 

(ii) 9650 × 27 

Rounding off 9650 to its greatest place i.e. hundreds place = 10000  Rounding off 27 to its greatest place i.e. tens place = 30  Hence, estimates 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 × 3491  

Rounding off 5281 to its hundreds place = 5300  

Rounding off 3491 to its hundreds = 3500  

Hence, estimates product = 5300 × 3500 = 1,85,50,000  

(ii) 1387 × 888  

Rounding off 1387 to its hundreds place = 1400  

Rounding off 888 to its hundreds = 900  

Hence, estimates product = 1400 × 900 = 12,60,000 

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 5709 when estimated to the nearest hundreds is ……. 

Solution:  

(i) The digits 2 has the highest place value in the number 2309.  (ii) The digits 9 has the highest face value in the number 2039.  

(iii) The digits 0 has the lowest face 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 5709 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 Internation system, a numbe 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 Internation system, a numbe 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 correst answer from the given four options ( 3 to 17):  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 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()) 

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 writtern 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 thedigit 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  

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 × 1000 + 850  

= 4850 m  

Distance travelled by Anu per day = 4850 m × 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. 

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 digits 2 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. 

Check your Progress  

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 two thousand three hundred   ninety four.  

Solution:  

(i) 6,09,00,047  

(ii) 104, 722, 394  

Question 2: Insert commas suitably and write the number 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  

72601  

 600  

 Face value of 6  

72601  

 6  

difference = 600  

 – 6  

 594  

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.  

Similarly, 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, alll 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, 3706, 59801, 560023  

Solution:  

3706, 58019, 3706, 59801, 560023  

Question 7.  

Write the greatest six-digit number using four different digits.  Solution:  

Greatest six-digits number using four different digits is 999876.  

Question 8.  

Write the smallest-eight 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 digits = 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.  

(i) 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 153m cloth,  how many uniforms can be stitched and how much cloth will remain ?  

Solution:  

Total cloth 153 m = 15300 cm  

To stitch a uniform, cloth needed  

= 1m 75cm = 175 cm  

Total uniforms can be stitched = ^+%,&& 

+-% 

= 87 ^-% 

+-% 

Hence, 87 uniforms can be stiched 75 cm cloth will remain extra.  

Question 14.  

Medicine is packed in boxes, each weighing 4 kg 500g. How many  such boxes can be loaded in a van which cannot carry beyond 800  kg?  

Solution:  

Weight of 1 box = 4 kg 500 gm  

= 4 × 1000 + 500 = 4500 gm  

Van can carry upto 800 kg  

= 800 × 1000 = 800000 gm  

Numbers of boxes that can be loaded in van 

= ^.&&&&&  

_$%&& = 117.8 i.e. 177 boxes  

A Van can 1c d 177 boxes of medicines.  

Question 15.  

Estimate : 6554 – 677 by estimating the numbers to their nearest  (i) thousands  

(ii) hundreds  

(iii) greatest places  

Also point out the most reasonable estimate.  

Solution:  

(i) Thousands ( 6554 – 677 )  

→ 7000 – 1000 = 6000  

(ii) Hundreds ( 6554 – 677)  

→ 6600 – 700 = 5900  

(iii) Greatest places ( 6554 – 677 )  

→ 7000 – 700 =6300 

Estimation to their nearest hundreds is most reasonable.