Get the simplified Class 7 Maths Extra Questions Chapter 1 Large Numbers Around Us Class 7 Extra Questions and Answers with complete explanation.
Class 7 Large Numbers Around Us Extra Questions
Class 7 Maths Chapter 1 Large Numbers Around Us Extra Questions
Class 7 Maths Chapter 1 Extra Questions
Question 1.
What are the smallest and largest 7-digit numbers?
Answer:
The smallest 7 -digit number is 10,00,000 and the largest 7-digit number is 99,99,999.
Reading and Writing of Large Numbers
We study the reading and writing of large numbers in two systems of naming numerals and placing commas
(i) Indian system
(ii) American or International system
In Indian system, we use ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakh, crores and so on. For the ease of writing and reading these large numbers, we place commas.
In Indian system, commas are placed to group the digits in 3-2-2-2-2-…… pattern from right to left (thousands, lakhs, crores, etc.)
e.g. We have a large number: 5080159234
In Indian system, 5080159234 can be written with commas as 5,08,01,59,234 and 5,08,01,59,234 can be read as five arab eight crore one lakh fifty-nine thousand two hundred thirty-four in Indian system.
In American system, we use ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million and so on. In American system, commas are placed to group the digits uniformly in 3-3-3-3-…..pattern from right to left (thousands, millions, billions, etc.)
e.g. We have a large number : 5080159234
In International system, 5080159234 can be written with commas as 5,080,159,234 and 5,080,159,234 can be read as five billion eighty million one hundred fifty-nine thousands two hundred thirty-four in International system.
The table below shows some numbers according to both the Indian system and the American system (also called the International system) of naming numerals and placing commas
Question 2.
Insert commas suitably in the following numbers and write their number names according to Indian system of numeration.
(i) 87595762
(ii) 8546283
(iii) 99900046
(iv) 98432701
Answer:
We can draw a table to show these operations
Question 3.
Insert commas suitably in the following numbers and write their number names according to International system of numeration.
(i) 78921092
(ii) 7452283
(iii) 99985102
(iv) 48049831
Answer:
We can draw a table to show these operations
Question 4.
Write the following numbers in Indian place value notation.
(i) Two crore thirty four lakh fifty six thousand seven hundred eighty nine.
(ii) Three billion three million three thousand three.
Answer:
(i) Here, in Indian place value notation, we have 2, 34, 56, 789.
(ii) Here, in Indian place value notation, we have 3,00,30,03,003.
Question 5.
Compare and write ‘ < ‘, ‘ > ‘ or ‘ = ‘.
(i) 50 thousand ….. 5 lakhs
(ii) 700 lakhs ….. 7 million
(iii) 900 thousands ….. 9 million
(iv) 550 crore ….. 50 billion
Solution:
(i) Here, 50 thousand = 50,000
and 5 lakhs = 5,00,000
∴ 50 thousand < 5 lakhs
(ii) Here, 700 lakhs = 70,000,000 and 7 million = 7,000,000
∴ 700 lakhs > 7 million
(iii) Here, 900 thousand = 900,000
and 9 million = 9,000,000
∴ 900 thousand < 9 million
(iv) Here, 550 crore = 5,500,000,000
and 50 billion = 50,000,000,000
∴ 550 crore < 50 billion
Question 6.
(i) A special calculator has only a + 1000 button. How many time should it be pressed to show :
(a) seventy-six thousand?
(b) 5,00,000 ?
Answer:
(a) Here, the + 1000 button should be pressed 76 times to show 76,000.
(b) Here, the + 1000 button should be pressed 500 times to show 5,00,000.
(ii) A special calculator has only a + 100 button. How many times should it be pressed to show
(a) 68,000 ?
(b) one million ?
Solution:
(a) Here, the + 100 button should be pressed 680 times to show 68,000.
(b) Here, the + 100 button should be pressed 10,000 times to show one million i.e. 1,000,000.
(iii) A special calculator has only a + 10 button. How many times should it be pressed to show
(a) two thousand ?
(b) 5,00,000 ?
Solution:
(a) Here, the + 10 button should be pressed 200 times to show 2,000.
(b) Here, the + 10 button should be pressed 50,000 times to show 5,00,000.
Question 7.
A special calculator has following buttons
+ 1, + 10, + 100, + 1,000, + 10,000, + 1,00,000, + 10,00,000.
(i) Give atleast two different ways to get 30,23,561.
(ii) Give a way to get the same number using as minimal number of clicks as possible.
Answer:
(i) The two of the many different ways to get 30,23,561 are shown below
(ii) Here, in order to get 30,23,561, using minimal number of clicks, the following clicks should be made
Question 8.
Round up 2,936 to the nearest
(i) thousands place value
(ii) hundreds place value
(iii) tens place value
Answer:
Given number is 2,936.
(i) Here, thousands place digit is 2.
∴ The given number 2,936 is rounded up to 3,000.
(ii) Here, hundreds place digit is 9.
∴ The given number 2,936 is rounded up to 3,000.
(iii) Here, tens place digit is 3.
∴ The given number 2,936 is rounded up to 2,940.
Question 9.
Round down 4,235 to the nearest
(i) thousands place value
(ii) hundreds place value
(iii) tens place value
Answer:
Given number is 4,235.
(i) Here, thousands place digit is 4.
∴ The given number 4,235 is rounded down to 4,000.
(ii) Here, hundreds place digit is 2.
∴ The given number 4,235 is rounded down to 4,200.
(iii) Here, tens place digit is 3.
∴ The given number 4,235 is rounded down to 4,230.
Nearest Neighbours
The nearest neighbours of a number are the nearest thousand, lakh or crore to that number.
e.g. The nearest neighbours of number 5,27,58,138 are shown in the table below
Question 10.
Write the five nearest neighbours for these numbers
(i) 9,23,45,678
(ii) 15,67,89,012
Answer:
(i) Given number is 9,23,45,678.
The nearest neighbours of the number 9,23,45,678 are given in the table below
(ii) Given number is 15,67,89,012.
The nearest neighbours of the number 15,67,89,012 are given in the table below
Estimating the Sum or Difference
To estimate or approximate sum or difference of two large numbers, we round up or down each term accordingly to the desired nearest neighbours and then calculate the sum or difference of rounded (or rounded off) terms.
Question 11.
Reema and Seema are estimating the value of a simple expression 2,34,567 + 3,45,678
Reema estimates, ‘The sum of near 5,00,000 and is less than 5,00,000.’
Seema estimates, ‘The sum is near 6,00,000 and is more than 6,00,000.’
(i) Are these estimates correct? Whose estimate is closer to the sum?
(ii) Will the sum be greater than 5,82,000 or less than 5,82,000 ? Why do you think so?
(iii) Will the sum be greater than 5,90,245 or less than 5,90,245 ? Why do you think so?
(iv) The exact value of 2 , 3 4 , 5 6 7 + 3 , 4 5 , 6 7 8 =…..
Answer:
We first round up or down accordingly to the nearest ten thousands.
∴ 2,34,567 is rounded up to 2,40,000 and 3,45,678 is rounded down to 3,40,000.
Now, adding these rounded numbers
2,40,000 + 3,40,000 = 5,80,000
(i) Clearly, this estimated sum is closer to 6,00,00,000 than 5,00,00,000.
∴ Seema’s estimation is correct and closer to the sum.
(ii) Clearly, the sum is less than 5,82,000 because the estimated sum 5,80,000 is less than 5,82,000.
(iii) Clearly, the sum is less than 5,90,245 because the estimated sum 5,80,000 is less than 5,90,245.
(iv) The exact value of 2,34,567 + 3,45,678 is 5,80,245.
Question 12.
Aadil and Aditya are estimating the value of a simple expression 7,89,123-2,34,567
Aadil estimates, ‘The difference is near 6,00,000 and is less than 6,00,000.’
Aditya estimates, ‘The difference is near 5,00,000 and is more than 5,00,000.’
(i) Are these estimates correct? Whose estimate is closer to the difference?
(ii) Will the difference be greater than 5,50,000 or less than 5,50,000 ? Why do you think so?
(iii) Will the difference be greater than 5,52,556 or less than 5,52,556 ? Why do you think so?
(iv) The exact value of 7,89,123-2,34,567 is……
Answer:
We first round up or down accordingly to the nearest ten thousands.
∴ 7,89,123 is rounded up to 7,90,000 and 2,34,567 is rounded down to 2,30,000.
Now, subtracting these rounded numbers
7,90,000 – 2,30,000 = 5,60,000
(i) Clearly, this estimated difference is closer to 6,00,000 than 5,00,000.
∴ Aadil’s estimation is correct and closer to the difference.
(ii) Clearly, the difference is greater than 5,50,000 because the estimated difference 5,60,000 is greater than 5,50,000.
(iii) Clearly, the difference is greater than 5,52,556 because the estimated difference 5,60,000 is greater than 5,52,556.
(iv) The exact value of 7,89,123-2,34,567 is 5,54,556.
Question 13.
Find quick ways to calculate these products.
(I) 4 × 1250 × 25
(ii) 36 × 250
(iii) 20 × 50 × 5
Answer:
(i) We have, 4 × 1250 × 25 = 4 × 1250 × \(\frac{100}{4}\)
= 1250 × 100
= 1,25,000
(ii) We have, 36 × 250 = 36 × \(\frac{1000}{4}\)
= 9000
(iii) We have, 20 × 50 × 5=20 × \(\frac{100}{2}\) × [/latex]\frac{10}{2}[/latex]
= 5 × 100 × 10
= 5000
Question 14.
Can multiplying a 6-digit number with a 3-digit number give a 10-digit number?
Answer:
We know that the multiplication of a m-digit number and a n-digit number will give either (m + n – 1)-digit number or (m + n) – digit number.
Here, m = 6, n = 3
∴ m + n – 1 = 6 + 3 – 1 = 8
and m + n = 6 + 3 = 9
∴ The multiplication of a 6-digit number with a 3-digit number can give either a 8 -digit number or a 9-digit number.
Hence, it cannot give a 10-digit number.
Large Numbers Around Us Extra Questions Class 7
Question 1.
What are the smallest and greatest 5 -digit numbers?
Answer:
10,000 and 99,999
Question 2.
Insert the commas suitably in the following numbers and write their number names according to Indian system
(i) 45623142
(ii) 300251070
Answer:
(i) 4,56,23,142; Four crore fifty six lakh twenty three thousand one hundred forty two.
(ii) 30,02,51,070 ; Thirty crore two lakh fifty one thousand seventy
Question 3.
Insert the commas suitably in the following numbers and write their number names according to American system
(i) 356298765
(ii) 400400404
Answer:
(i) 356,298,765, Three hundred fifty six million two hundred ninety eight thousand seven hundred sixty five.
(ii) 400,400,404; Four hundred million four hundred thousand four hundred four.
Question 4.
Write the following numbers in Indian place value notation.
(i) Twenty crore thirty lakh forty thousand fifty.
(ii) Seven billion sixty million five hundred thousand four hundred.
Answer:
(i) 20,30,40,050
(ii) 7,06,05,00,400
Question 5.
Compare the following and write ‘ < ‘, ‘ > ‘, or ‘ = ‘.
(i) 50 lakhs….. 5 million
(ii) 3 crore….. 300 million
(ii) 10 crore….. 10 million
(iv) 1,00,000….. 1 lakh
Answer:
(i) =
(ii) <
(iii) >
(iv) =
Question 6.
(i) A special calculator has only a + 1000 button. How many times should it be pressed to show
(a) five crores?
(b) five lakh five thousand?
Answer:
(a) 50,000
(b) 505
(ii) A special calculator has only a + 100 button. How many times should it be pressed to show
(a) 1 billion?
(b) one million one hundred?
Answer:
(a) 10,000,000
(b) 10,001
(iii) A special calculator has only a + 10 button. How many times should it be pressed to show
(a) 56,79,000 ?
(b) eighty thousand?
Answer:
(a) 5,67,900
(b) 8,000
Question 7.
A special calculator has the following buttons
+ 1, + 10, + 100, + 1,000, + 10,000, + 1,00,000, + 10,00,000.
(i) Give atleast two different expressions to get 4,05,60,301.
(ii) Give a expression to get the same number using as minimal number of clicks as possible.
Question 8.
Round up and down the number 6,73,15,042 to the nearest
(i) thousand place value
(ii) ten thousand place value
(iii) lakh place value
(iv) crore place value
Answer:
Round up
(i) 6,73,16,000
(ii) 6,73,20,000
(iii) 6,74,00,000
(iv) 7,00,00,000
Round down
(i) 6,73,15,000
(ii) 6,73,10,000
(iii) 6,73,00,000
(iv) 6,00,00,000
Question 9.
Write the five nearest neighbours of 4 , 3 2 , 5 6 , 7 2 1.
Answer:
Nearest thousand: 4,32,57,000
Nearest ten thousand : 4,32,60,000
Nearest lakh : 4,33,00,000
Nearest ten lakh : 4,30,00,000
Nearest crore : 4,00,00,000
Question 10.
Rina and John are estimating the values of the simple expressions
A. 5 , 2 5 , 3 2 0 + 3 , 8 1 , 4 5 0
Rina, ‘The sum is near 9,00,000 and is less than 9,00,000.’
John, ‘The sum is near 9,10,000 and is more than 9,00,000.’
(i) Are these estimates correct? Whose estimate is closer to the sum?
(ii) Will the sum be greater than 9,05,000 or less than 9,05,000 ? Why?
(iii) Will the sum be greater than or less than 9,07,770? Why?
(iv) Exact value of 5,25,320 + 3,81,450 is……
Answer:
(i) John’s estimation is closer to sum.
(ii) greater than
(iii) less than
(iv) 9,06,770
B. 1 2 , 4 5 , 7 8 0 – 2 , 5 0 , 6 0 0
Rina, ‘The difference is near 10,00,000 and is less than 10,00,000.’
John, ‘The difference is near 9,95,000 and is more than 9,90,000.’
(i) Are these estimates correct? Whose estimate is closer to the sum?
(ii) Will the difference be greater or less than 9,90,000 ? Why?
(iii) Will the difference be greater or less than 9,98,180 ? Why?
(iv) Exact value of 12,45,780-2,50,600 iş
Answer:
(i) John’s estimate is closer to difference
(ii) greater than
(iii) less than
(iv) 9,95,180
Question 11.
Find quick ways to calculate these products.
(i) 25 × 125 × 2
(ii) 50 × 4 × 385
(iii) 41276 × 50
Answer:
(i) 6,250
(ii) 77,000
(iii) 20,63,800
Question 12.
Can multiplying a 3-digit number with a 3-digit number give a 5-digit number?
Answer:
Yes