RD Sharma Solutions Class 6 Maths Chapter 1 Knowing our Numbers

EXERCISE 1.1

Question 1:  Write each of the following in numeral form:

i) Eight thousand twelve

ii) Seventy thousand fifty-three

iii) Five lakh seven thousand four hundred six

iv) Six lakh tow thousand nine

v) Thirty lakh eleven thousand one

vi) Eight crore four lakh twenty-five.

vii) Three crore three thousand three hundred three

viii) Seventeen crores sixty lakh thirty thousand fifty-seven.

Solution 1:

Question 2:  Write the following numbers in words in the Indian system of numeration.

(i) 42,007

(ii) 4,05,045

(iii) 35,42,012

(iv) 7,06,04,014

(v) 25,05,05,500

(vi) 5,50,50,050

(vii) 5,03,04,012 

Solution 2:

Question 3:   Insert commas in the correct positions to separate periods and write the following numbers in words:

i) 4375

ii) 24798

iii) 857367

iv) 9050784

v) 10105607

vi) 10000007

vii) 910107104 

Solution 3:

Question 4: Write each of the following in expanded form:

i) 3057

ii) 12345

iii) 10205

iv) 235060 

Solution 4:

Question 5:  Write the corresponding numeral for each of the following:

i) 7 x 10000 + 2 x 1000 + 5 x 100 + 9 x 10 + 6 x 1

ii) 4 x 100000 + 5 x 1000 + 1 x 100 + 7 x 1

iii) 8 x 1000000 + 3 x 1000 + 6 x 1

iv) 5 x 10000000 + 7 x 1000000 + 8 x 1000 + 9 x 10 + 4 

Solution 5:

Question 6:   Find the place value of the digit 4 in each of the following:

i) 74983160

ii) 8745836 

Solution  6:

i) Place value of 4 in the number 7,49,83,160 is = 10,00,000 × 4= 40,00,000

ii) Place value of 4 in the number 87,45,836 is = 10,000 × 4 = 40,000

Question 7:  Determine the product of the place values of two fives in 450758. 

Solution  7:

Place value of first 5 = 10 × 5  = 50

Place value of second 5 = 10,000 × 5 = 50,000

So, the Required product = 50 × 50,000 = 25,00,000

Question 8:  Determine the difference of the place values of 7’s in 257839705. 

Solution  8:

Place value of first 7 = 10 × 7 = 700

Place value of second 7 = 10,000 × 7 = 70,00,000

So, the difference = 70,00,000 – 700 = 69,99,300

Question 9:  Determine the difference between the place value and the face value of 5 in 78654321. 

Solution  9:

Place value of 5 = 10,000 × 5 = 50,000

Face value of 5 = 5

So, the difference = 50,000 – 5 = 49,995

Question 10:  Which digits have the same face value and place value in 92078634? 

Solution  10:   In Number 9,20,78,634 digit 4 on once place have same place and face value & digit 0 has same place value and face value.

Question 11:   How many different 3 digit numbers can be formed by using the digits 0, 2, 5 without repeating any digit in the number? 

Solution  11:   205, 250, 520 and 502 are three-digit numbers formed using the digits 0, 2 and 5 without repeating any digit in the number.

Question 12:  Write all possible 3- digit numbers using 6, 0, 4 when

i) Repetition of digits is not allowed

ii) Repetition of digits is allowed 

Solution 12:       

i) Numbers Without Repetition:- 604, 640, 460, 406.

ii) Numbers With Repetition:- 666, 664, 646, 660, 606, 600, 644, 640, 604, 444, 466, 440, 446,464, 400, 404, 406, 460.

Question 13:   Fill in the blanks:

Solution 13:       

EXERCISE 1.2

Question 1:  Write each of the following numbers in digits by using international place value chart. Also, write them in expanded form.

i) Seven million three hundred three thousand two hundred six

ii) Fifty five million twenty nine thousand seven

iii) Six billion one hundred ten million three thousand seven 

Solution 1:

Question 2:  Rewrite each of the following numerals with proper commas in the international system of numeration

i) 513625

ii) 4035672

iii) 65954923

iv) 70902005 

Solution 2:

Question 3:  Write each of the following numbers in the international system of numeration:

(i) Forty three lakh four thousand eighty four.

(ii) Six crore thirty four lakh four thousand forty four.

(iii) Seven lakh thirty five thousand eight hundred ninety nine only. 

Solution 3:

Question 4:   Write the following numbers in the Indian system of numeration:

(i) Six million five hundred forty three thousand two hundred ten.

(ii) Seventy six million eighty five thousand nine hundred eighty seven

(iii) Three hundred twenty five million four hundred seventy nine thousand eight hundred thirty eight. 

Solution 4:

Question 5:  A certain nine digit number has only ones in one’s period, only twos in the thousands period and only threes in millions periods. Write this number in words in the Indian system. 

Solution  5:

Nine digit numbers has only ones in one’s period, only twos in the thousands period and only threes in millions periods is 333,222,111.

In numbers it is written as 33,32,22,111.

Indian System it is written as “Thirty three crore thirty two lakh twenty thousand one hundred eleven”.

Question: 6:   How many thousands make a million? 

Solution   6:    1,000 thousands make a million

Question 7:  How many millions make a billion? 

Solution  7:  1,000 millions make a billion

Question 8:

(i) How many lakhs make a million?

(ii) How many lakhs make billion? 

Solution 8:

(i) 10 lakhs make a million

(ii) 10,000 lakhs make a billion

Question 9:  Write each of the following in numerical form:

(i) Nighty-Eight million seven hundred eight thousand four.

(ii) Six hundred seven million twelve thousand eighty four.

(iii) Four billion twenty five million forty five thousand. 

Solution 9:

Question 10:  Write the number names of each of the following in international system of numeration:

(i) 435,002

(ii) 1,047,509

(iii) 59,064,523

(iv) 25,201,905 

Solution 10:

EXERCISE 1.3

Question 1:  How many four – digit numbers are there in all? 

Solution 1:

Lowest 4 digit Number = 1000

0 to 999 upto 3 digit Numbers.

Largest 4 digit Number = 9999

Four digit numbers are in all = 9999 – 999 = 9000

Therefor, 9000 four-digit numbers are there in all.

Question 2:  Write the smallest and the largest six digit numbers. How many numbers are between these two? 

Solution 2:

The smallest six digit number = 100000

The largest six digit number = 999999

Required difference = 999999 – 100000 = 899999

89999 numbers are between in these two.

Question 3:  How many 8 – digit numbers are there in all? 

Solution 3:  

Largest 8 digit Number = 99999999

Largest 7 digit Number = 9999999

8-digit numbers are in all = 99999999 – 9999999 = 90000000

Therefor, 90000000 eight-digit numbers are there in all.

Question 4:  Write 10075302 in words and rearrange the digits to get the smallest and the largest numbers. 

Solution  4:  Digits in 10075302 are 0, 1, 2, 3, 5 and 7.

Smallest 8-digit number by using digits 0, 1, 2, 3, 5 and 7 = 1,00,02,357.

Largest 8-digit number by using digits 0, 1, 2, 3, 5 and 7 = 7,53,21,000.

Put the smallest digit 1 at highest place value and largest digit 7 at Last place value.

Put the Largest digit 7 at highest place value and smallest digit 0 at Last place value.

Question 5:  What is smallest 3-digit number with unique digits? 

Solution  5:  102 is the smallest three-digit number with unique digits.

Question 6:  What is the largest 5- digits number with unique digits?  

Solution  6:  98,765 is largest 5- digit number with unique digits.

Question 7: Write is smallest 3-digit number which does not change if the digits are written in reverse order. 

Solution  7:  101 is smallest 3-digit number that does not change if the digits are written in reverse order.

Question 8:   Find the difference between the number 279 and that obtained on reversing its digits. 

Solution  8:   Given number = 279

Number obtained on reversing = 972

Difference = 972 – 279 = 693

So, the difference between 279 and that obtained on reversing it is 693.

Question 9:  Form the largest and smallest 4- digit numbers using each of digits 7,1,0,5 only once. 

Solution  9:

Given digits 7,1,0 and 5.

The largest four- digit numbers formed using 7,1,0 is = 7,510

The smallest four- digit numbers formed using 7,1,0 is = 1,057

EXERCISE 1.4

Question 1:  Put the appropriate symbol ( < > ) in each of the following boxes :

(i) 102394 ___ 99887

(ii) 2507324 ___ 2517324

(iii) 3572014 ____ 10253104

(iv) 47983505 ____ 47894012 

Solution 1:

Question 2:  Arrange the following numbers in ascending order:

(i) 6,35,47,201, 10,23,45,694 , 65,39,542 , 83,54,208 , 1,23,45,678

(ii) 18,08,088, 1,81,888, 1,90,909, 18,08,090, 1,60,60,666 

Solution 2:

(i) 65,39,542 < 83,54,208 < 1,23,45,678 < 6,35,47,201 < 10,23,45,694 

(ii) 1,81,888 < 1,90,909 < 18,08,088 < 18,08,090 < 1,60,60,666

Question 3:  Arrange the following numbers in descending order:

(i) 5,69,44,000, 5,69,43,201, 56,95,440, 5,69,43,300, 56,94,437

(ii) 10,20,216, 10,20,308, 10,21,430, 8,93,425, 8,93,245 

Solution 3:

i) 5,69,44,000 > 5,69,43,300 > 5,69,43,201 > 56,95,440 > 56,94,437 

ii) 10,21,430 > 10,20,308 > 10,20,216 > 8,93,425 > 8,93,245

EXERCISE 1.5

Question 1:  How many milligrams make one kilogram? 

Solution 1:  10,00,000 (Ten lakh) milligrams make one kilogram.

Question 2:  A box of medicine tablets contains 2,00,000 tablets each weighing 20mg. what is the total weight of all the tablets in the box in grams? in kilograms ? 

Solution 2:

Given that each tablet weights = 20mg

Weight of 2,00,000 tablets = 2,00,000 × 20 = 40,00,000 mg

The total weight of all the tablets in the box = 40,00,000 mg 

Question 3:  Population of Sundar Nagar was 2,35,471 in the year 1991. In the year 2001 it was found to have increased by 72,958. What was the population of the city in 2001? 

Solution 3:

Population of Sundar Nagar in 1991 = 2,35,471 

Population of Sundar Nagar in 2001 = Population of Sundar Nagar in 1991 + Increase in population

Population of Sundar Nagar in 2001 = 2,35,471 + 72,958

Population of Sundar Nagar in 2001= 3,08,429

Question 4:  A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final days were respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days.

Solution 4: 

Total number of tickets sold on all four days is:

Total Number of tickets = 1094 + 1812 + 2050 + 2751

Total Number of tickets = 7707

Question 5:  The town newspaper is published every day. One copy has 12 pages. Everyday 11,980 copies are printed. How many pages are in all printed every day? Every month? 

Solution 5:

Number of pages in a copy of newspaper = 12 

Number of pages in 11,980 copies of newspaper = 11,980 × 12 = 1,43,760

So, 1,43,760 pages are printed every day. 

Therefore, Number of pages printed in a month = 1, 43,760 × 30 = 43, 12,800

So, 43, 12,800 pages are printed in a month.

Question 6:  A machine, on an average, manufactures 2825 screws a day. How many screws did it produce in the month of January 2006? 

Solution  6:

Number of screws produced by a machine in a day = 2,825

Number of days in January = 31

Number of screws produced by the same machine in the month of January 2006 is

Number of screws = 2,825 × 31 = 87,575

Thus, Machine-produced 87,575 screws in the month of January 2006.

Question 7:  A famous cricket player has so far scored 6978 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need? 

Solution 7:

Runs scored by cricket player in test matches = 6,978

Required to complete runs = 10,000

Remaining runs = 10,000 – 6,978 = 3,022

Therefore, 3,022 more runs to complete 10,000 runs.

Question 8:  Ravish has Rs. 78,592 with him. He placed an order for purchasing 39 radio sets at Rs. 1234 each. How much money will remain with him after the purchase? 

Solution 8:

Total money with Ravish’s = Rs.78, 592

Price of 1 radio = Rs. 1,234

Price of 39 such radio = Rs. 1,234 × 39 = Rs. 48,126

Therefore, Money spent by him on purchasing 39 radio sets Rs. 48,126

Remaining money with him after the purchasing = Money with him – Money spent on 39 radio sets

Remaining Money = Rs. 78,592 – Rs. 48,126

Remaining Money = Rs. 30,466

Therefore, Money left after purchases is Rs. 30,466.

Question 9:  In an election, the successful candidate registered 5,77,570 votes and his nearest rival secured 3,48,685 votes. By what margin did the successful candidate win the election? 

Solution 9:

Votes registered by the winner = 5,77,570

Votes secured by the rival = 3,48,685

Winning Margin = 5,77,570 – 3,48,685

Winning Margin = 2,28,885

Therefore, Margin of victory for the successful candidate 2,28,885

Question 10:  To stitch a shirt 2m 15 cm cloth is needed. Out of 40 m cloth, how many shirts can be stitched and how much cloth will remain? 

Solution 10:

Question 5: Round off the following measures to the nearest hundreds:

(i) Rs. 666

(ii) Rs. 850

(iii) Rs. 3,428

(iv) Rs. 9,080

(v) 1265 km

(vi) 417 m

(vii) 550 cm

(viii) 2486 m

(ix) 360 gm

(x) 940 kg

(xi) 273 l

(xii) 820 mg 

Solution 5:

(i) Rs. 700

(ii) Rs. 900

(iii) Rs. 3,500

(iv) Rs. 9100

(v) 1300 km

(vi) 400 m

(vii) 600 cm

(viii) 2500 m

(ix) 400 gm

(x) 900 kg

(xi) 300 l

(xii) 800 mg

Question 6:  List all numbers which are rounded off to the nearest ten as 370. 

Solution 6:  Numbers are rounded off to the nearest ten as 370:- 365, 366, 367, 368, 369, 370, 371, 372, 373, 374.

Question 7:  Find the smallest and the greatest numbers which are rounded off to the nearest hundreds as 900. 

Solution 7:

Smallest number: 850

Greatest number: 949

Question 8:  Find the smallest and the greatest numbers which are rounded off to the nearest thousands as 9000. 

Solution 8:

Smallest number: 8,500

Greatest number: 9,499

EXERCISE 1.7 

Question 1:  Estimate the following by rounding off each factor to nearest hundreds:

(i) 730 + 998

(ii) 796 – 314

(iii) 875 – 384 

Solution 1:

(i) Rounded off nearest hundreds of 730 is = 700

Rounded off nearest hundreds of 998 is = 1,000

So, the rounded off of 730 + 998 = 700 + 1000 = 1700

(ii) Rounded off nearest hundreds of 796 is = 800

Rounded off nearest hundreds of 314 is = 300

So, the rounded off of 796 - 314 = 800 - 300 = 500

(iii) Rounded off nearest hundreds of 875 is = 900

Rounded off nearest hundreds of 384 is = 400

So, the rounded off of 875 – 384 = 900 - 400 = 500

Question 2:  Estimate the following by rounding off each factor to nearest thousands:

(i) 12904 + 2888

(ii) 28292 – 21496 

Solution 2:

(i) Rounded off nearest thousands of 12,904 is = 13,000

Rounded off nearest thousands of 2,888 is = 3,000

So, the rounded off of 12904 + 2888 = 13,000 + 3,000 = 16,000

(ii) Rounded off nearest thousands of 28,292 is = 28,000

Rounded off nearest thousands of 21,496 is = 21,000

So, the rounded off of 28292 – 21496 = 28,000 + 21,000 = 7,000

Question 3:  Estimate the following by rounding off each number to its greatest place:

(i) 439 + 334 + 4317

(ii) 8325 – 491

(iii) 108734 – 47599

(iv) 898 × 785

(v) 9 × 795

(vi) 87 × 317 

Solution 3:

(i) Round off of 439 in its greatest place is = 400

Round off of 334 in its greatest place is = 300

Round off of 4317 in its greatest place is = 4000

Estimate 400 + 300 + 4000 = 4700

(ii) Round off of 8325 in its greatest place is = 8000

Round off of 491 in its greatest place is = 500

Estimate 8000 - 500 = 7500

(iii) Round off of 108734 in its greatest place is = 1,00,000

Round off of 47599 in its greatest place is = 50,000

Estimate 1,00,000 – 50,000 = 50,000

(iv) Round off of 898 in its greatest place is = 900

Round off of 785 in its greatest place is = 800

Estimate 900 × 800 = 7,20,000

(v) Round off of 9 in its greatest place is = 10

Round off of 795 in its greatest place is = 800

Estimate 9 × 795 = 8,000

(vi) Round off of 87 in its greatest place is = 90

Round off of 317 in its greatest place is = 300

Estimate 90 × 300 = 27,000

Question 4:  Find the estimated quotient for each of the following by rounding off each number to its greatest place:

(i) 878 ÷ 28

(ii) 745 ÷ 24

(iii) 4489 ÷ 394

Solution 4: