Experts have designed these Class 7 Maths Notes and Chapter 1 Large Numbers Around Us Class 7 Notes for effective learning.
Class 7 Maths Chapter 1 Notes Large Numbers Around Us
Class 7 Maths Notes Chapter 1 – Class 7 Large Numbers Around Us Notes
A Lakh Varieties! Class 7 Notes
In previous classes, we have become familiar with numbers. We have used the numbers and have learned many things about them. Numbers help us count objects. We can identify which collection of objects is bigger with the help of numbers. We can arrange the numbers in order. We can use the numbers in different contexts and numerous ways.
Introducing 1,00,000
The smallest 2-digit number is 10.
The greatest 2-digit number is 99.
The smallest 3-digit number is 100.
The greatest 3-digit number is 999.
The smallest 4-digit number is 1000.
The greatest 4-digit number is 9999.
We find an interesting pattern if we add 1 to the greatest number of 1-digit, the greatest number of 2-digit, tand he greatest number of 3-digit numbers as follows:
9+ 1 = 10 = 10 × 1
99 + 1 = 100 = 10 × 10
999 + 1 = 1000 = 10 × 100
It shows that
Greatest single digit number + 1 = Smallest 2-digit number
Greatest 2-digit number + 1 = Smallest 3-digit number
Greatest 3-digit number + 1 = Smallest 4-digit number.
It suggests that if we add 1 to the greatest 4-digit number, i.e., 9999, we get the smallest 5-digit number, i.e., 10000 (ten thousand).
Thus, 9999 + 1 = 10000 = 10 × 1000.
The greatest 5-digit number is 99999. If we add 1 to it, we get the smallest 6-digit number, which is 1,00,000. Then, 99999 + 1 = 1,00,000
The number 1,00,000 is named as one lakh. It comes next to 99,999.
Large Numbers
The greatest 6-digit number is 9,99,999. If we add 1 to it, we get the smallest 7-digit number, which is 10,00,000. Thus, 9,99,999 + 1 = 10,00,000
The number 10,00,000 is named as ten lakh. It comes next to 9,99,999.
The greatest 7-digit number is 99,99,999. If we add 1 to it, we get the smallest 8-digit number, which is 1,00,00,000. Thus, 99,99,999 + 1 = 1,00,00,000.
The number 1,00,00,000 is named as one crore. It comes next to 99,99,999.
1 hundred = 10 tens
1 thousand = 10 hundreds = 100 tens
1 lakh = 100 thousands = 1,000 hundreds = 10,000 tens
1 crore = 100 lakhs = 10,000 thousands = 1,00,000 hundreds = 10,00,000 tens
Reading and Writing Large Numbers
Reading and writing large numbers involve understanding place value and grouping digits into periods like ones, thousands, and millions. In the Indian system, commas are used to separate periods of hundreds, thousands, lakhs, and crores. In the International system, commas separate periods of ones, thousands, millions, and billions.
Example 1.
Write the names of the following numbers:
(i) 12,78,830
(ii) 15,75,000
(iii) 1,234,567
(iv) 4,567,890,123
Solution:
(i) 12,78,830: Read as “twelve lakh seventy-eight thousand eight hundred thirty” (using the Indian place value system).
(ii) 15,75,000: Read as “fifteen lakh seventy-five thousand” (using the Indian place value system).
(iii) 1,234,567: Read as “one million two hundred thirty-four thousand five hundred sixty-seven” (using the International place value system).
(iv) 4,567,890,123: Read as “four billion five hundred sixty-seven million eight hundred ninety thousand one hundred twenty-three”(using the International place value system).
Example 2.
Write the corresponding number in the Indian place value system for each of the following:
(a) Five lakh twenty-four thousand four hundred and fifty-four
(b) Six lakh seven thousand eight hundred and four
(c) Eighty lakhs five thousand and fifty
(d) Twenty lakhs two hundred and thirty-five
Solution:
(a) Five lakh twenty-four thousand four hundred and fifty-four = 5,24,454
(b) Six lakh seven thousand eight hundred and four = 6,07,804
(c) Eighty lakhs five thousand and fifty = 80,05,050
(d) Twenty lakhs two thousand three hundred and thirty five = 20,02,335
In the Indian numbering system, a lakh is a relatively large number, equivalent to 100,000 in the International System of Units. It’s used to express quantities like money, population, or land area. For example, a salary of 1 lakh rupees per month is considered a decent income in India.
Land of Tens Class 7 Notes
In “Land of Tens,” we explore numbers using place value, focusing on how numbers are built up in groups of 10, 100, 1000, and so on. This concept is used to represent and manipulate larger numbers efficiently.
Of Crores and Crores! Class 7 Notes
Indian System of Numeration
In this system, we get ones, tens, hundreds, thousands, and then lakhs and crores. Commas are used to mark thousands, lakhs, and crores.
See examples:
(i) 4,09,02,387 = Four crore nine lakh two thousand three hundred eighty seven
(ii) 5,43,50,699 = Five crore forty three lakh fifty thousand six hundred ninety nine
The first comma comes after the hundreds place (three digits from the right) and marks thousands.
The second comma comes after the thousands place (five digits from the right) and marks lakh.
The third comma comes after the ten lakh place (seven digits from the right) and marks a crore.
Note: We do not use commas while writing number names.
International System of Numeration
In this system, we have ones, tens, hundreds, thousands, and then millions.
Note that 1 million = 1 thousand thousands = 10 lacs
See examples:
(i) 41,713,644 = Forty-one million seven hundred thirteen thousand six hundred forty-four.
(ii) 33,602,751 = Thirty-three million six hundred two thousand seven hundred fifty-one.
Commas are used to mark thousands and millions. It comes after every three digits from the right.
The first comma marks thousands.
The second comma marks millions.
Note 1: We do not use commas while writing number names.
Note 2: 1 billion = 1000 million
Relation between the Indian and International Systems of Numeration
Question 1.
Place commas correctly and write the numerals:
(a) Seventy-three lakh seventy-five thousand three hundred seven
(b) Nine crore five lakh forty-one
(c) Seven crore fifty-two lakh 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.
Solution:
(a) Seventy three lakh seventy five thousand three hundred seven = 73,75,307
(b) Nine crore fifty lakh forty-one = 9,50,00,041
(c) Seven crore fifty two lakh twenty one thousand three hundred two = 7,52,21,302
(d) Fifty-eight million four hundred twenty-three thousand two hundred two = 58,423,202
(e) Twenty-three lakh thirty thousand ten = 23,30,010
Question 2.
(a) Insert commas suitably and write the names according to the Indian system of Numeration:
(i) 87595762
(ii) 99900046
(b) Insert commas suitably and write the names according to the international system of Numeration:
(i) 99985102
(ii) 48049831
Solution:
(a) (i) 87595762 = 8,75,95,762
Eight crore seventy-five lakh ninety-five thousand seven hundred sixty-two
(ii) 99900046 = 9,99,00,046
Nine crore ninety-nine lakh forty-six
(b) (i) 99985102 = 99,985,102
Ninety-nine million nine hundred eighty-five thousand one hundred two
(ii) 48049831 = 48,049,831
Forty-eight million forty-nine thousand eight hundred thirty-one
Exact and Approximate Values Class 7 Notes
There are a number of situations when we do not need the exact number but only a rough estimate of a number. For example, if we arrange a big celebration at our home, then we find out roughly how many guests may attend the celebration. It is practically impossible to give an idea of the exact number of visitors. Estimation means approximating a quantity to the desired accuracy. So, before estimation, we must know how to round olla given number.
Estimating to the Nearest Tens by Rounding Off
Numbers I to 4 are nearer to 0 than to 10. So, 1, 2, 3, and 4 are rounded off as 0.
Numbers 6 to 9 are nearer to 10 than to 0. So 6, 7, 8, and 9 are rounded off as 10.
Number 5 is equidistant from 0 and 10. So 5 is rounded off to 10 customarily.
Thus, 12, 25, and 17 are rounded off as 10, 30, and 20, respectively.
Estimating to the Nearest hundreds by Rounding Off
Numbers 1 to 49 are closer to 0 than to 100, and so are rounded off to 0. Numbers 51 to 99 are closer to 100 than to 0, and so are rounded off to 100. Number 50 being equidistant from 0 and 100, both, it is rounded off to 100 customarily. Thus, 212, 375, and 495 are rounded off as 200, 400, and 500, respectively.
Estimating to the Nearest Thousands by Rounding Off
Numbers 1 to 499 are nearer to 0 than to 1000 and so are rounded off to 0. Numbers 501 to 999 are nearer to 1000 than to 0 and so are rounded off to 1000.
Number 500 is equidistant from 0 and 1000. So it is rounded off to 1000 customarily. Thus, 1445, 3333, and 6889 are rounded off as 1000, 3000, and 7000, respectively.
Note 1: For rounding off a number to the nearest tens, we examine the digit at the ones place.
If the digit at the ones place is less than 5, then we replace the ones digit with 0 and keep all other digits as they are.
If the digit at the ones place is 5 or more, then we replace the ones digit with 0 and increase the tens digit by 1.
Note 2: For rounding off a number to the nearest hundred, we examine the digit at the tens place.
If the digit at the tens place is less than 5, then we replace the digits at the tens place and ones place each with 0 and keep all other digits as they are.
For example, 123 → 100.
If the digit at the tens place is 5 or more, then we replace the tens digit and the ones digit each by 0, and increase the digit at the hundreds place by 1.
For example, 153 → 200.
Note 3: For rounding off a number to the nearest thousand, we examine the digit at the hundreds place.
If the digit at the hundreds place is less than 5, then we replace the digits at the hundreds place, tens place, and ones place each with 0 and keep all other digits as they are.
For example, 1450 → 1000.
If the digit at the hundreds place is 5 or more, then we replace each one of the digits at the hundreds place, tens place, and ones place with 0 and increase the digit at the thousands place by 1.
For example, 1650 → 2000.
Example 1.
Estimate 5,180 + 17,875 to the nearest thousand.
Solution:
5,180, when rounded off to thousands, becomes 5000.
17,87,5 when rounded off to thousands becomes 18000.
∴ Estimate sum = 5000 + 18000 = 23000.
Example 2.
Estimate 5,790 – 472 to the nearest hundred.
Solution:
5790 rounded off to hundreds becomes 5800.
472 rounded off to hundreds becomes 500.
∴ Estimated difference = 5800 – 500 = 5300.
Solved Examples
Question 1.
Give a rough estimate (by rounding off to the nearest hundreds) and also a closer estimate (by rounding off to the nearest tens):
(a) 439 + 334 + 4,317
(b) 1,08,734 – 47,599
Solution:
(a) (i) Rough estimate (by rounding off to nearest hundreds) = 400 + 300 + 4,300 = 5,000
(ii) Rough estimate (by rounding off to nearest tens) = 440 + 330 + 4,320 = 5090
(b) (i) Rough estimate (by rounding off to nearest hundreds) = 1,08,700 – 47,600 = 61,100
(ii) Rough estimate (by rounding off to nearest tens) = 1,08,730 – 47,600 = 61,130
Question 2.
Estimate the following sums as directed:
(a) 378 + 243 to the nearest tens
(b) 385 + 254 to the nearest hundred
(c) 32489 + 38908 + 53606 to the nearest thousands
Solution:
(a) 378 estimated to the nearest tens = 380
243 estimated to the nearest tens = 240
∴ Required estimation = 380 + 240 = 620
(b) 385 estimated to the nearest hundreds = 400
254 estimated to the nearest hundreds = 300
∴ Required estimation = 400 + 300 = 700
(c) 32469 estimated to the nearest thousands = 32000
38908 estimated to the nearest thousands = 39000
53606 estimated to the nearest thousands = 54000
∴ Required estimation = 32000 + 39000 + 54000 = 125000
Question 3.
(a) Estimate the following products by rounding off each factor to the nearest tens: 38 × 73
(b) Estimate the following products by rounding off each factor to the nearest hundred: 493 × 249
(c) Estimate the following product by rounding off each factor to its greatest place: 4826 × 5937
Solution:
(a) 38 rounded off to the nearest tens = 40
73 rounded off to the nearest tens = 70
∴ Required estimation = 40 × 70 = 2800
(b) 493 rounded off to the nearest hundred 500
249 rounded off to the nearest hundred = 200
∴ Required estimation = 500 × 200 = 100000
(c) Each factor is a 4-digit number.
So, we round off each factor to the nearest thousand.
4826 rounded off to the nearest thousand = 5000
5937 rounded oil to the nearest thousand = 6000
∴ Required estimation 5,000 × 6,000 = 3,00,00,000
Roxie and Estu are Estimating the Values of Simple Expressions
1. 4,63,128 + 4,19,682
Roxie: “The sum is nearly 8,00,000 and is more than 8,00,000.”
Estu: “The sum is nearly 9,00,000 and is less than 9,00,000.”
(a) Are these estimates correct? Whose estimate is closer to the sum?
Solution:
The estimate is correct.
(b) Will the sum be greater than 8,50,000 or less than 8,50,000? Why do you think so?
Solution:
Yes, it would be more than 8,50,000 because if we add the first 2 digits from left, the sum is 87, which is greater than 85.
(c) Will the sum be greater than 8,83,128 or less than 8,83,128? Why do you think so?
Solution:
The sum would be less than 8,83,128.
(d) Exact value of 4,63,128 + 4,19,682 = ________________
Solution:
Exact value of 463128 + 419682 = 8,82,810
2. 14,63,128 – 4,90,020
Roxie: “The difference is nearly 10,00,000 and is less than 10,00,000.”
Estu: “The difference is nearly 9,00,000 and is more than 9,00,000.”
(a) Are these estimates correct? Whose estimate is closer to the difference?
Solution:
Exact difference = 14,63,128-4,90,020 = 9,73,108
Estimated difference = 15,00,000 – 5,00,000 = 10,00,000
Roxie’s estimate is closer to the actual difference.
(b) Will the difference be greater than 9,50,000 or less than 9,50,000? Why do you think so?
Solution:
Exact difference = 9,73,108
It is greater than 9,50,000.
Now estimating the numbers 14,63,128 and 4,90,020 to the nearest ten thousands place, we get 14,60,000 and 4,90,000 respectively.
Now, Difference = 14,60,000 – 4,90,000 = 9,70,000
It is more than 9,50,000.
(c) Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think so?
Solution:
Exact difference is 9,73,108
It is greater than 9,63,128.
Difference = 9,73,108 – 9,63,128 = 9,980
It is far from the actual difference.
(d) Exact value of 14,63,128 – 4,90,020 = ________________
Solution:
Exact value = 4,63,128 – 4,90,020 = 9,73,108
Patterns in Products Class 7 Notes
In mathematics, a “Pattern in Products” refers to identifying and understanding the relationships between the factors and the resulting product of multiplication. Patterns in products can be used to simplify calculations, solve equations, and make predictions.