# NCERT Solutions for Class 6 Maths Chapter 1: Knowing our Numbers

In this page we have NCERT Solutions for Class 6 Maths Chapter 1: Knowing our Numbers Exercise 1.1,1.2,1.3 with try these also. Hope you like them and do not forget to like , social share and comment at the end of the page.

## Exercise 1.1

Question 1
Fill in the blanks:
(a). 1 lakh = _________ ten thousand.
(b). 1 million = _________ hundred thousand.
(c). 1 crore = _________ ten lakhs.
(d). 1 crore = _________ million.
(e). 1 million = _________ lakh.
Answer
a) 1 lakh = _10___ ten thousand
1 lakh = 1,00,000
= 100 thousand
= 10 ten thousand
(b). 1 million = ____10_____ hundred thousand.
1 million    = 1,000,000
= 1000 thousand
= 10 hundred thousand
(c). 1 crore = _______10__ ten lakhs.
1 crore = 1,00,00,000
= 100 lakhs
= 10 ten lakh
(d). 1 crore = ______10___ million.
1 crore = 1,00,00,000
Adding commas to the number 10000000 according to the International system, we have
10,000,000 = 10 million
1 crore = 10 million
(e). 1 million = ____10_____ lakh.
1 million = 10,000,000
Adding commas to the number 10000000 according to the Indian system, we have
1,00,00,000 = 1 crore = 100 lakhs
1 million = 100 lakh
Question 2
Place commas correctly and write the numerals:
(a)Seventy-three lakh seventy-five thousand three hundred seven.
(b)Nine crore five lakhs forty-one.
(c)Seven crore fifty-two lakhs twenty-one thousand three hundred two.
(d)Fifty-eight million four hundred twenty-three thousand two hundred two.
(e)Twenty-three lakh thirty thousand ten.
Answer
(a) $73,75,307$
(b) $9,05,00,041$
(c) $7,52,21,302$
(d) $58,423,202$
(e) $23,30,010$

Question 3
Insert commas suitably and write the names according to Indian System of Numeration:
(a) $87595762$
(b) $8546283$
(c) $99900046$
(d) $98432701$
Answer
 A 8,75,95,762 Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two B 85,46,283 Eighty-five lakh forty-six thousand two hundred eighty-three C 9,99,00,046 Nine crore ninety-nine lakh forty-six D 9,84,32,701 Nine crore eighty-four lakh thirty-two thousand seven hundred one

Question 4:
Insert commas suitably and write the names according to International System of Numeration:
(a) $78921092$
(b) $7452283$
(c) $99985102$
(c) $48049831$
Answer
 A 78,921,092 Seventy-eight million nine hundred twenty-one thousand ninety-twos B 7,452,283 Seven million four hundred fifty-two thousand two hundred eighty-threes C 99,985,102 Ninety-nine million nine hundred eighty-five thousand one hundred twos D 48, 049,831 Forty-eight million forty-nine thousand eight hundred thirty-ones

## Exercise 1.2

Question 1
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 day was respectively 1094, 1812, 2050, and 2751. Find the total number of tickets sold on all the four days.
Answer
Given
Number of tickets sold at the counter on 1st day = 1094
Number of tickets sold at the counter on 2nd day = 1812
Number of tickets sold at the counter on 3rd day = 2050
Number of tickets sold at the counter on 4th day = 2751
Total Number of tickets sold on all the four days = 1094 + 1812 + 2050 + 2751
=7707
Question 2
Shekhar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10, 000 runs. How many more runs does he need?
Answer
Runs scored as of now= 6980
Runs Shekhar wishes to score = 10,000
No of runs required Shekhar need to achieve his wish = Runs Shekhar wants to score - Runs scored so far    =10,000 – 6980 =3020
So ,Shekhar need 3,020 more runs to achieve his target
Question 3
In an election, the successful candidate registered 5, 77, 500 votes and his nearest rival secured 3, 48, 700 votes. By what margin did the successful candidate win the election?
Answer
Votes registered by successful candidate = 5,77,500
Votes registered by rival = 3,48,700
Margin will be given by = 5,77,500 − 3,48,700
=228800
So, Margin = 2,28,800
Question 4
Kirti book store sold books worth Rs 2,85,891 in the first week of June and books worth Rs 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?
Answer
Value of Books sold in 1st week of June = Rs 2,85,891
Value of books sold in 2nd week of June = Rs 4,00,768
Total sale of books of two weeks = Sale in 1st week + Sale in 2nd week = 2,85,891 + 4,00,768
=6,86,659
The sale for the two weeks together was 6,86,659.
Since 4,00,768 > 2,85,891, sale in 2nd week was greater than 1st week.
Now difference would be
=4,00,768 - 2,85,891 = 1,14,877
The sale in 2nd week was larger than the sale in 1st week by Rs 1,14,877.
Question 5
Find the difference between the greatest and the least number that can be written using the digits 6, 2, 7, 4, 3 each only once.
Answer
The digits to be used are 6,2,7,4,3
The greatest number can be obtained by writing the digits from the largest to smallest i.e., 7 6 4 2 3
Greatest number will be= 76432
The least number is obtained by writing the digits from smallest to largest i.e., 2 3 4 6 7
Smallest number will be= 23467
Difference = 76432 − 23467
=52,965
Therefore,the difference between the greatest and the least number using the nunber given above is 52,965.
Question 6
A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?
Answer
Given Screws produced the machine in one day = 2,825
Now we know that Days in the month of January = 31
Screws produced in Jan 2006(31 days )= $2825 \times 31 = 87575$
Question 7
A merchant had Rs 78,592 with her. She placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after the purchase?
Answer
One radio set cost= Rs 1200
40 radio sets will cost= $1200 \times 40$= Rs 48000
Money with Merchant = Rs 78,592
Money spent for purchasing 40 radio sets = Rs 48,000
Money left = (Money with Merchant) – (Money spent on radio sets)
=78592 − 48000 =30592
Question 8
A student multiplied 7236 by 65 instead of multiplying by 56. By how much was his answer greater than the correct answer? (Hint: Do you need to do both the multiplications?)
Answer
Difference between 65 and 56 = 9
Difference in the answer = 7236 × 9
=65124
We can double check using 7236 × 65 = 4,70,340 and 7236 × 56 = 4,05,216.
Difference is =4,70,340 - 4,05,216
=65,124
Therefore, the answer was greater than the correct answer by 65,124
Question 9
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? (Hint: convert data in cm.)
Answer
First convert both the data given into same units
As 1 m = 100 cm
Cloth needed to stitch one shirt=2 m 15 cm = 215 cm
Total cloth present=40 m = $40 \times 100$ = 4000 cm
Total Number of shirts that can be stitched out of 4000 cm = 4000 ÷ 215

So, 18 shirts can be made. Remainder will be 130 cm, i.e. 1 m 30 cm, cloth will remain.
Question 10
Medicine is packed in boxes, each weighing 4 kg 500 g. How many such boxes can be loaded in a van which cannot carry beyond 800 kg?
Answer
First convert into same unit As 1 kg = 1000 g
So ,Weight of one box=4 kg 500 g = 4500 g
Also Total capacity of the VAN= 800 kg = $800 \times 1000$ = 800000 g
Number of Medicine boxes that can be loaded in the van = 800000 ÷ 4500

So ,it can be observed that 177 boxes at maximum can be loaded in the van.
Question 11
The distance between the school and the house of a student’s house is 1 km 875 m. Every day she walks both ways. Find the total distance covered by her in six days.
Answer
Distance between the school and the house = 1 km 875 m
Now, 1 km = 1000 m
1 km 875 m = 1875 m
Distance travelled each day =2 × distance between school and house= 1875 × 2 = 3750 m
Distance travelled in 6 days = 3750 × 6 =22500 m
= 22.5 km or 22 km 500 m
Question 12
A vessel has 4 liters and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
Answer
Converting into same units (1 L = 1000 ml)
Capacity of vessel = 4 L 500 ml = 4500 ml
Capacity of one glass = 25 ml
Number of glasses that can be filled with curd = 4500 ÷ 25

So, 180 glasses can be filled.

## Exercise 1.3

Question 1
Estimate each of the following using general rule:
(a) $730 + 998$
(b) $796 - 314$
(c) $12, 904 + 2, 888$
(d) $28, 292 - 21, 496$
Make ten more such examples of addition, subtraction and estimation of their outcome.
Answer
(a) $730 + 998$
Rounding off to nearest hundreds we get   730 rounds off to 700 and 998 rounds off to 1000.
$=700 + 1000=1700$
(b) $796 - 314$
Rounding off to nearest hundreds, we get 796 rounds off to 800 and 314 rounds off to 300.
$=800-300=500$
(c) $12904 + 2822$
Rounding off to nearest thousands, we get 12904 rounds off to 13000 and 2822 rounds off to 3000.
$=13000+ 3000=16000$

(d) $28,296 - 21,496$
Rounding off to nearest thousands, we get 28296 rounds off to 28000 and 21496 rounds off to 21000.
$=28000-21000=7000$
Question 2
Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
(a) $439 + 334 + 4, 317$
(b) $1,08, 734 - 47, 599$
(c) $8325 - 491$
(d) $4, 89, 348 - 48, 365$
Make four more such examples.
Answer
(a) $439 + 334 + 4317$
Rounding off to nearest hundreds, 439, 334, and 4317 may be rounded off to 400, 300, and 4300 respectively.
So sum would be $=400+300+4300=5000$
Rounding off to nearest tens, 439, 334, and 4317 may be rounded off to 440, 330, and 4320 respectively.
So sum would be =440+330+4320=5090

(b) 1,08,734 − 47,599
Rounding off to hundreds, 1,08,734 and 47,599 may be rounded off to 1,08,700 and 47,600 respectively.
So difference would be= 108700-47600=61100
Rounding off to tens, 1,08,734 and 47,599 may be rounded off to 1,08,730 and 47,600 respectively.
So difference would be=108730-47600=61130

(c) $8325 - 491$
Rounding off to hundreds, 8325 and 491 may be rounded off to 8300 and 500 respectively.
Difference would be =8300-500=7800
Rounding off to tens, 8325 and 491 may be rounded off to 8330 and 490 respectively.
Difference would be=8330-490=7840
(d) 4,89,348 − 48,365
Rounding off to hundreds, 489348 and 48365 may be rounded off to 489300 and 48400 respectively.
Difference would be=489300-48400=440900
Rounding off to tens, 489348 and 48365 may be rounded off to 489350 and 48370 respectively.
Difference would be= 489350-48370=440980

Question 3
Estimate the following products using general rule:
(a) $578 \times 161$
(b) $5281 \times 3491$
(c) $1291 \times 592$
(d) $9250 \times 29$
Answer
(a) $578 \times 161$
Rounding off by general rule, 598 and 161 may be rounded off to 600 and 200 respectively.
$600 \times 200=120000$

(b) $5281 \times 3491$
Rounding off by general rule, 5281 and 3491 may be rounded off to 5000 and 3000 respectively.
$5000 \times 3000= 15000000$

(c) $1291 \times 592$
Rounding off by general rule, 1291 and 592 may be rounded off to 1000 and 600 respectively.
$1000 \times 600=600000$

(d) $9250 \times 29$
Rounding off by general rule, 9250 and 29 may be rounded off to 9000 and 30 respectively.
$9000 \times 30=270000$

## Try these solutions from NCERT book

Question 1
Can you instantly find the greatest and the smallest numbers in each row?
1. 382, 4972, 18, 59785, 750.
Ans. 59785 is the greatest and 18 is the smallest.
2. 1473, 89423, 100, 5000, 310.
Ans. 89423 is the greatest and 100 is the smallest.
3. 1834, 75284, 111, 2333, 450 .
Ans. 75284 is the greatest and 111 is the smallest.
4. 2853, 7691, 9999, 12002, 124
Ans. 12002 is the greatest and 124 is the smallest.

Was that easy?
Yes it was easy

Why was it easy?
The greatest number has the most thousands and the smallest is only in hundreds or in tens.

Question 2
Find the greatest and the smallest numbers.
(a) 4536, 4892, 4370, 4452.
(b) 15623, 15073, 15189, 15800.
(c) 25286, 25245, 25270, 25210.
(d) 6895, 23787, 24569, 24659
Answer
a. 4892 is the greatest and 4370 is the smallest.
b. 15800 is the greatest and 15073 is the smallest.
c. 25286 is the greatest and 25210 is the smallest.
d. 24659 is the greatest and 6895 is the smallest.

Question 3. Use the given digits without repetition and make the greatest and smallest 4-digit numbers.
(a) 2, 8, 7, 4
(b) 9, 7, 4, 1
(c) 4, 7, 5, 0
(d) 1, 7, 6, 2
(e) 5, 4, 0, 3
(Hint : 0754 is a 3-digit number.)
Answer
For greatest, we need to arranges digit in decreasing order and for smallest, in increasing order
a. Greatest:8742 ,Smallest:2478
b. Greatest:9741 ,Smallest:1479
c. Greatest:7540 ,Smallest:4057
d. Greatest:7621 ,Smallest:1267
e. Greatest:5430 ,Smallest:3045

Question 4.
Now make the greatest and the smallest 4-digit numbers by using any one digit twice.
(a) 3, 8, 7
(b) 9, 0, 5
(c) 0, 4, 9
(d) 8, 5, 1
(Hint : Think in each case which digit will you use twice.)
Answer
Here for greatest, largest digit will be used twice, and for smallest, smallest digit will be used twice
a. Greatest:8873 ,Smallest:3378
b. Greatest:9950 ,Smallest:5009
c. Greatest:9940 ,Smallest:4009
d. Greatest:8851 ,Smallest:1158

Question 5.
Make the greatest and the smallest 4-digit numbers using any four different digits with conditions as given.
(a) Digit 7 is always at ones place
Greatest: 9867
Smallest:1027
(b) Digit 4 is always at tens place
Greatest:___
Smallest: ___
(c) Digit 9 is always at hundreds place
Greatest:____
Smallest:____
(d) Digit 1 is always at thousands place
Greatest:____
Smallest:____
Answer:
b.
Greatest:9847
Smallest: 1042
c.
Greatest:8976
Smallest:1902
d.
Greatest:1987
Smallest:1023

Question 6. Take two digits, say 2 and 3. Make 4-digit numbers using both the digits equal number of times.
Which is the greatest number?
Which is the smallest number?
How many different numbers can you make in all?
Answer
Greatest: 3322
Smallest :2233
Total number : 6

Question 7
How many milligrams make one kilogram?
Answer
1 kg=1000000 mg
Question 8.
A box contains 2,00,000 medicine tablets each weighing 20 mg. What is the total weight of all the tablets in the box in grams and in kilograms?
Answer
Total Weight = 200000 * 20 = 4000000 mg = 4 kg

Question 8
A bus started its journey and reached different places with a speed of 60 km/hour. The journey is shown below.

(i) Find the total distance covered by the bus from A to D.
(ii) Find the total distance covered by the bus from D to G.
(iii) Find the total distance covered by the bus, if it starts from A and returns back to A.
(iv) Can you find the difference of distances from C to D and D to E?
(v)Find out the time taken by the bus to reach
(a) A to B (b) C to D
(c) E to G (d) Total journey
Answer
i. Total distance covered by the bus from A to D = 4170 + 3410 + 2160 = 9740 km
ii. total distance covered by the bus from D to G=8140+4830 +2550=15,520 km
iii. total distance covered by the bus, if it starts from A and returns back to A
= Total distance covered by the bus from A to D + total distance covered by the bus from D to G + distance covered from G to A
= 9740+15,520 +1290=26550 km
iv. As seen from the figure,distance from C to D=2160 km
Distance from D to E = 8140 km
v. Now it is given bus speed is 60 km/hr which means it covers 60 km in 1 hr.
a. Distance from A to B=4170 km
So time taken = $4170 \div 60$ = 69 hour 30 min
b. Distance from C to D=2160 km
So time taken = $2160 \div 60$ = 36 hour
c. Total distance covered from E to G = 4830 + 2550=7380 km
So time taken = $7380 \div 60$ = 123 hour
d. Now Total journey distance= 26550 km
So time taken = $26550 \div 60$ = 442 hour 30 min

Question 9

a. Can you find the total weight of apples and oranges Raman sold last year?
Weight of apples = __________ kg
Weight of oranges = _________ kg
Therefore, total weight = _____ kg + _____ kg = _____ kg
(b) Can you find the total money Raman got by selling apples?
(c) Can you find the total money Raman got by selling apples and oranges together?
(d) Make a table showing how much money Raman received from selling each item. Arrange the entries of amount of money received in descending order. Find the item which brought him the highest amount.How much is this amount?
Answer
a.
Weight of apples = 2457 kg
Weight of oranges = 3004 kg
Answer – The total weight of oranges and apples = 5461 kg.
b. Apple cost is Rs 40 per kg
Total apple sold =2457 kg
Money made= 40 * 2457= Rs 98280
c. Orange cost is Rs 30 per kg
Total oranges sold= 3004 kg
Money made= 30 * 3004 = 90120
Total money Raman got by selling Apple and Oranges = 98280 + 90120=Rs 188,440
d.
Here is the table which shows money Raman received from selling each item

Descending order
253670 , 240012,160040,98280,90120,68280,38530
Item which brought the highest amount is tooth brush and amount is Rs 253670

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### Practice Question

Question 1 What is $\frac {1}{2} + \frac {3}{4}$ ?
A)$\frac {5}{4}$
B)$\frac {1}{4}$
C)$1$
D)$\frac {4}{5}$
Question 2 Pinhole camera produces an ?
A)An erect and small image
B)an Inverted and small image
C)An inverted and enlarged image
D)None of the above

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