Large Numbers Around Us Class 7 Notes Maths Chapter 1

Students often refer to Class 7 Maths Notes and Chapter 1 Large Numbers Around Us Class 7 Notes during last-minute revisions.

Class 7 Maths Chapter 1 Notes Large Numbers Around Us

Class 7 Maths Notes Chapter 1 – Class 7 Large Numbers Around Us Notes

→ We are surrounded by numbers, and they serve countless purposes. Having previously worked with numbers up to hundreds and thousands, focusing on their uses, notation, patterns, and exact approxitnate calculations. In this chapter, we will learn about large numbers like lakhs and crores. We will understand how big these numbers are, where we use them, and how to write and read them. We will also explore patterns in numbers and learn to find exact and approximate values using simple and fun methods.

→ We encounter large numbers such as akhs and crores, as well as millions and billions. We learn how to read and write these numbers in both the Indian and International systems.

• 1 lakh is written as 1 followed by 5 zeros: 1.00,000
• 1 crore is written as I followed by 7 zeros: 1.00.00,000
• 1 million is written as I followed by 6 zeros: 1.000,000 (which is also equal to ten lakhs)
• 1 billion is written as 1 followed by 9 zeros: 1.000.000.000 (which is also equal to 100 crores)

→ To understand large numbers or quantities, we compare them with smaller, familiar numbers to get a clear sense of how much bigger they are. This helps us discover some fascinating facts about large numbers.

→ Approximation is a calculation or rounding off the number to the nearest value, making the calculation easy.

→ We came across large numbers — lakhs, crores, and arabs; millions and billions.

→ We learnt how to read and write these numbers in the Indian and American/International naming systems.

→ 1 lakh is 1 followed by 5 zeroes: 1,00,000

→ 1 crore is 1 followed by 7 zeroes: 1,00,00,000

→ 1 million is 1 followed by 6 zeroes: 1,000,000 (which is also ten lakhs)

→ 1 arab is 1 followed by 9 zeroes: 1,000,000,000 (which is also 100 crore or 1 billion)

→ We generally round up or round down large numbers. It is often enough to know roughly how big or small something is.

→ To get a sense of large numbers or quantities, we can check how many times bigger they are compared to numbers or quantities that are more familiar.

→ We saw how to factorise numbers and regroup them to simplify multiplications.

→ We carried out interesting thought experiments, such as “Would one be able to watch 1000 movies in a year?”

Large Numbers

→ The numbers beyond thousands are called large numbers. These are used in real life to count populations, money, distances, etc.
e.g.

• Lakh A lakh is the smallest 6 – digit number which is written as 1,00,000.
• Crore A crore is nothing but 100 lakhs which is written as 1,00,00,000.
• Arab An arab is 100 crores which is written as 1,00,00,00,000.

→ Formation of the Smallest and the Largest n – digit numbers

• The smallest n – digit number is formed by writing 1 followed by (n – 1) zeroes.
• e.g. The smallest 3 – digit number is formed by writing 1 and then followed by 3 – 1 = 2 zeroes i.e. 100.
• The largest or greatest n – digit number is formed by writing n 9 s.
• e.g. The largest 3 – digit number is formed by writing 39 s. i.e. 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

• Indian system
• 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

Land of Tens

→ In the Land of tens, there are special calculators with only one type of button – each adding a specific value like + 10, + 100 or + 1000.

→ This concept helps students to understand how large numbers can be formed by repeated addition.

→ Types of calculators in Land of Tens

• Tedious Tens It has only a + 10 button, which adds 10 by pressing it once.
  e.g. For 3,000 , the + 10 button is pressed 300 times.
• Handy Hundreds It has only a + 100 button, which adds 100 by pressing it once.
  e.g. For 3,000 , the + 100 button is pressed 30 times.
• Thoughtful Thousands It has only a + 1000 button, which adds 1000 by pressing it once.
  e.g. For 3,000, the + 1000 button is pressed three times.
• Creative Chitti It has + 1, + 10, + 100, + 1000, + 10,000, + 1,00,000, + 10,00,000 buttons, which can create same numbers using different combinations. e.g. For 321,32 × (+ 10) + 1 × (+ 1) or 2 × (+ 100) + 12 × (+ 10) + 1 × (+ 1)

Approximation and Patterns in Products

Exact Value

The true or accurate value of mathematical quantity is called as exact value.
e.g. √25 = 5

Approximated Value

→ The value of a mathematical quantity which is close to the exact value but not exactly equal to the exact value, is called as an approximated value.

→ e.g. The approximate value of √2 is 1.414.

Rounding Up and Down

→ Sometimes exact numbers are not required, just an approximation is sufficient.

→ The process of adjusting a number to an approximate value is called as rounding (or rounding off).

→ We do the rounding in two ways

• Rounding up
• Rounding down

→ Rounding up a number means increasing the number to the closest desired place value.

→ Rounding down a number means decreasing the number to the closest desired place value.

→ e.g. If a school has 732 people including students, teachers and staff, the principal might order 750 sweets instead of 700 sweets.

→ e.g. If the cost of an item is ₹ 470, then the shopkeeper may say that the cost is around ₹ 450 instead of saying it is around ₹ 500.

Note

• Rounding up is when the approximated number is more than the actual number.
• Rounding down is when the approximated number is less than the actual number.

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

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.

Multiplication Shortcut

→ There is an easy way to multiply numbers like 5, 25, 50, 250, 125 etc using the following shortcuts

→ To multiply by 5 , divide the number by 2 and then multiply by 10.
e.g. We have,
116 × 5 = (116 + 2) × 10
= 58 × 10
= 580

→  To multiply by 25 , divide the number by 4 and then multiply by 100.
e.g. We have,
824 × 25 = (824 ÷ 4) × 100
= 206 × 100
= 20,600

→ To multiply by 50 , divide the number by 2 and then multiply by 100.
e.g. We have,
2502 × 50 = (2502 + 2) × 100
= 1251 × 100
= 125100

→ To multiply by 125, divide the number by 8 and then multiply 1000.
e.g.
We have,
824 × 125 = (824 + 8) × 1000
= 103 × 1000
= 1,03,000

→ To multiply by 250, divide the number by 4 and then multiply 1000.
e.g. We have,
824 × 250 = (824 + 4) × 1000
= 206 × 1000
= 2,06,000

Pattern in Products

→ We can identify how long a multiplication of two numbers can be.

→ If a m – digit number is multiplied with a n – digit number, then the product will have either (m + n – 1) – digit number or (m + n) – digit number.

→ e.g. If we multiply 10,00,231 × 52, then the product will be either 7 + 2 – 1 = 8 – digit number or 7 + 2 = 9 – digit number.

→ Since, 10,00,231 × 52 = 5,20,12,012 which is a 8 – digit number.
Hence, it is verified.

A Lakh Varieties! Class 7 Notes

Eshwarappa is a farmer in Chintamani, a town in Karnataka. He visits the market regularly to buy seeds for his rice field. During one such visit, he overheard a conversation between Ramanna and Lakshmamma. Ramanna said, “Earlier, our country had about a lakh varieties of rice. Farmers used to preserve different varieties of seeds and use them to grow rice. Now, we only have a handful of varieties. Also, farmers have to come to the market to buy seeds”.

Lakshmamma said, “There is a seed bank near my house. So far, they have collected about a hundred indigenous varieties of rice seeds from different places. You can also buy seeds from there.” You may have heard the word ‘lakh’ before. Do you know how big one lakh is? Let us find out.

Eshwarappa shared this incident with his daughter, Roxie, and son Estu. Estu was surprised to know that there were about one lakh varieties of rice in this country. He wondered, “One lakh! So far, I have only tasted 3 varieties. If we tried a new variety each day, would we even come close to tasting all the varieties in a lifetime of 100 years?” What do you think? Guess. But how much is one lakh?

Roxie and Estu found that if they ate one variety of rice a day, they would come nowhere close to a lakh in a lifetime! Roxie suggests, “What if we ate 2 varieties of rice every day? Would we then be able to eat 1 lakh varieties of rice in 100 years?”

What if a person ate 3 varieties of rice every day? Will they be able to taste all the lakh varieties in a 100-year lifetime? Find out.
Estu said, “We know how many days there are in a year — 365, if we ignore leap years. If we live for y years, the number of days in our lifetime will be 365 × y.”

1. The smallest 6-digit number is 1,00,000 (‘1’ followed by five zeroes).
It is read as ‘one lakh’.

2. The largest 6-digit number is 9,99,999.

3. 9,99,999 + 1 = 10,00,000.
This is the smallest 7-digit number. (‘1’ followed by six zeroes)
It is read as ‘ten lakh’.

4. The largest 7-digit number is 99,99,999.

5. A feel of large numbers

• The head of an adult human being has about one lakh hair.
• If I walk 10 km a day, it will take more than 27 years to walk one lakh kilometers.
• The cost of a new car is around ? 12 lakh.

6. Reading and writing numbers
While writing a number in figures commas are placed to group the digits in a 3-2-2-2… pattern from right to left. This makes reading the number easier.
Any number written in figures can be written in words (number name of the number).

• 4, 25, 500 : Four lakh twenty-five thousand five hundred.
• 12, 30, 820 : Twelve lakh thirty thousand eight hundred and twenty.

Getting a Feel of Large Numbers
You may have come across interesting facts like these:

• The world’s tallest statue is the ‘Statue of Unity’ in Gujarat, depicting Sardar Vallabhbhai Patel. Its height is about 180 metres.
• Kunchikal waterfall in Karnataka is said to drop from a height of about 450 metres.

It is not always easy to get a sense of how big these measurements are. But we can get a better sense of their size when we compare them with something familiar.

Is One Lakh a Very Large Number?
Eshwarappa asked Roxie and Estu, “Is a lakh big or small?”

Roxie feels that 1 lakh is a large number:

• “We had one lakh varieties of rice — that is a lot.”
• “Living 1 lakh days would mean living for 274 years—that is a long time!”
• “If 1 lakh people stood shoulder to shoulder in a line, they could stretch as far as 38 kilometres.”

Estu, however, thinks it is not that big:

• “Do you know that the cricket stadium in Ahmedabad has a seating capacity of more than 1 lakh? One lakh people in such a small area!”
• “Most humans have 80,000 to 1,20,000 hairs on their heads. Imagine, 1 lakh hairs fit in such a tiny space!”
• “I heard that there are some species of fish where a female fish can lay almost one lakh eggs at once, very comfortably. Some even lay tens of lakhs of eggs at a time.”

Reading and Writing Numbers
We have already been using commas for 5-digit numbers like 45,830 in the Indian place value system. As numbers grow bigger, using commas helps in reading the numbers easily. We use a comma in between the digits representing the “ten thousands” place and the “one lakh” place, as you have seen just before (1,00,000). The number name of 12,78,830 is twelve lakh seventy eight thousand eight hundred thirty. Similarly, the number 15,75,000 in words is fifteen lakh seventy-five thousand.

Land of Tens Class 7 Notes

Systematic Sippy is a different kind of calculator. It has the following buttons: +1, +10, +100, +1000, +10000, +100000. It wants to be used as minimally as possible.

What if we press the +10,00,000 button ten times? What number will come up? How many zeroes will it have? What should we call it?
The number will be 100 lakhs, which is also called a crore. 1 crore is written as 1,00,00,000—it is 1 followed by seven zeroes.

Any number can be expressed as a combination of ones, tens, hundreds, etc. in more than one way.
32 = 10 + 10 + 10 + 1 + 1 (three tens, and two ones)
32 = 10 + 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 (two tens, and twelve ones)
430 can be expressed as a sum of 4 hundreds, and 3 tens.
430 can also be expressed as a sum of 3 hundreds, and 13 tens. There are more ways.
7650 can be expressed as a sum of 7 thousands, 6 hundreds, and 5 tens.
7650 can also be expressed as a sum of 7 thousands, 5 hundreds, and 15 tens. There are more ways.

Of Crores and Crores! Class 7 Notes

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. Observe the placement of commas in both systems.

Indian System		American System
1,000	One thousand	1,000	One thousand
10,000	Ten thousand	10,000	Ten thousand
1,00,000	One lakh	100,000	Hundred thousand
10,00,000	Ten lakhs	1,000,000	One million
1,00,00,000	One crore	10,000,000	Ten million
10,00,00,000	Ten crores	100,000,000	Hundred million
1,00,00,00,000	One Arab or One Hundred Crores	1,000,000,000	One billion

Notice that in the Indian system, commas are placed to group the digits in a 3-2-2-2… pattern from right to left (thousands, lakhs, crores, etc.). In the American system, the digits are grouped uniformly in a 3-3-3-3… pattern from right to left (thousands, millions, billions, etc.).

The Indian system of naming numbers is also followed in Bhutan, Nepal, Sri Lanka, Pakistan, Bangladesh, the Maldives, Afghanistan, and Myanmar. The words lakh and crore originate from the Sanskrit words lakṣha (लक्ष and koṭi (कोटि‍). The American system is also used in many countries.
Observe the number of zeroes in 1 lakh and 1 crore.

• 1 lakh, written in numbers, would be 1 followed by 5 zeroes.
• 1 crore, written in numbers, would be 1 followed by 7 zeroes.

A lakh is a hundred times a thousand, a crore is a hundred times a lakh, and an arab is a hundred times a crore (i.e., a hundred thousand is 1 lakh, 100 lakhs is 1 crore, and 100 crores is 1 arab).

1. 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.

Indian System		American System
1,000	One thousand	1,000	One thousand
10,000	Ten thousand	10,000	Ten thousand
1,00,000	One lakh	100,000	Hundred thousand
10,00,000	Ten lakh	1,000,000	One million
1,00,00,000	One crore	10,000,000	Ten million
10,00,00,000	Ten crore	100,000,000	Hundred million
1,00,00,00,000	One arab or one hundred crore	1,000,000,000	One billion

2. In the Indian system, commas are placed to group the digits in a 3-2-2-2… pattern from right to left (thousands, lakhs, crores, etc.).

• 1 lakh, written in numbers would be 1 followed by 5 zeroes.
• 1 crore, written in numbers would be 1 followed by 7 zeroes.
• 100 thousand is 1 lakh, 100 lakh is 1 crore, and 100 crore is 1 arab.

3. In the American system, the digits are grouped uniformly in a 3-3-3-3… pattern from right to left (thousands, millions, billions, etc.).

• 1 million, written in numbers would be 1 followed by 6 zeroes.
• 1 billion, written in numbers would be 1 followed by 9 zeroes.
• 1000 thousand is 1 million, 1000 million is 1 billion.

4. We note that 1 arab is the same as 1 billion.

Exact and Approximate Values Class 7 Notes

What do you think of this conversation? Have you read or heard such headlines or statements?
Very often, exact numbers are not required and just an approximation is sufficient. For example, according to the 2011 census, the population of Chintamani town is 76,068. Instead, saying that the population is about 75,000 is enough to give an idea of how big the quantity is.

There are situations where it makes sense to round up a number (rounding up is when the approximated number is more than the actual number).
For example, if a school has 732 people, including students, teachers, and staff, the principal might order 750 sweets instead of 700 sweets.

There are situations where it is better to round down (rounding down is when the approximated number is less than the actual number).
For example, if the cost of an item is ₹470, the shopkeeper may say that the cost is around ₹450 instead of saying it is around ₹500.

1. Very often, exact numbers are not required and just an approximation is sufficient.

2. There are situations where it makes sense to round up a number (rounding up is when the approximated number is more than the actual number).

3. There are situations where it is better to round down (rounding down is when the approximated number is less than the actual number).

4. With large numbers, it is useful to know the nearest thousand, lakh, or crore.

Nearest Neighbours
With large numbers it is useful to know the nearest thousand, lakh or crore. For example, the nearest neighbours of the numbers 6,72,85,183 are shown in the table below.

Nearest thousand	6,72,85,000
Nearest ten thousand	6,72,90,000
Nearest lakh	6,73,00,000
Nearest ten lakh	6,70,00,000
Nearest crore	7,00,00,000

Patterns in Products Class 7 Notes

Roxie and Estu are playing with multiplication. They encounter an interesting technique for multiplying a number by 10, 100, 1000, and so on.

Large Number Fact
In a single gram of healthy soil, there can be 100 million to 1 billion bacteria and 1 lakh to 1 million fungi, which can support plants’ growth and health. Share such large-number facts you know/come across with your class.

1. If a number is multiplied by 5, 25, … a shortcut can be applied.

2. Let us multiply 116 by 5.

= 58 × 10
= 580.
5 is replaced by \(\frac{10}{2}\). We note that 116 is divisible by 2.

3. Let us multiply 824 by 25.

= 20600.
25 is replaced by \(\frac{100}{4}\). We note that 824 is divisible by 4.

4. How many digits in the product?

• 24 × 25 = 600 (2-digit × 2-digit = 3-digit)
• 74 × 85 = 6290 (2-digit × 2-digit = 4-digit)
• Hence 2-digit × 2-digit = 3-digit number or 4-digit number

(Note that: 2 + 2 – 1 = 3 and 2 + 2 = 4)

In the same way,

• 3-digit × 3-digit = 5-digit number or 6-digit number,
• 4-digit × 5-digit = 8-digit number or 9-digit number, etc.

A Multiplication Shortcut
Roxie evaluated 116 × 5 as follows:
116 × 5 = 116 × \(\frac{10}{2}\)
= 58 × 10
= 580

Estu evaluated 824 × 25 as follows:
824 × 25 = 824 × \(\frac{100}{4}\) = 20600

Fascinating Facts about Large Numbers
Some interesting facts about large numbers are hidden below. Calculate the product or quotient to uncover the facts. Once you find the product or quotient, read the number in both Indian and American naming systems. Share your thoughts and questions about the fact with the class after you discover each number.

1250 × 380 is the number of kirtanas composed by Purandaradasa according to legends. Purandaradasa was a composer and singer in the 15th century. His kirtanas spanned social reform, bhakti, and spirituality. He systematised methods for teaching Carnatic music, which are followed to the present day.

2100 × 70,000 is the approximate distance in kilometers, between the Earth and the Sun. This distance keeps varying throughout the year. The farthest distance is about 152 million kilometers.

6400 × 62,500 is the average number of litres of water the Amazon River discharges into the Atlantic Ocean every second. The river’s flow into the Atlantic is so much that drinkable freshwater is found even 160 kilometers into the open sea.

As you did before, divide the given numbers to uncover interesting facts about division. Share your thoughts and questions with the class after you uncover each number.

13,95,000 ÷ 150 is the distance (in kms) of the longest single-train journey in the world. The train runs in Russia between Moscow and Vladivostok. The duration of this journey is about 7 days. The longest train route in India is from Dibrugarh in Assam to Kanyakumari in Tamil Nadu; it covers 4219 kms in about 76 hours.

Adult blue whales can weigh more than 10,50,00,000 ÷ 700 kilograms. A newborn blue whale weighs around 2,700 kg, which is similar to the weight of an adult hippopotamus. The heart of a blue whale was recorded to be nearly 700 kg. The tongue of a blue whale weighs as much as an elephant. Blue whales can eat up to 3500 kg of krill every day. The largest known land animal, Argentinosaurus, is estimated to weigh 90,000 kg.

52,00,00,00,000 ÷ 130 was the weight, in tonnes, of global plastic waste generated in the year 2021.

Did You Ever Wonder…? Class 7 Notes

Estu is amused by all these interesting facts about large numbers. While thinking about these, he came up with an unusual question, “Could the entire population of Mumbai fit into 1 lakh buses?” What do you think? How can we find out?

Let us assume a bus can accommodate 50 people. Then 1 lakh buses can accommodate 1 lakh × 50 = 50 lakh people.

The population of Mumbai is more than 1 crore 24 lakhs. So, the entire population of Mumbai cannot fit in 1 lakh buses.

1. Facts about large numbers can leave us wondering.

2. Let us consider the following:

• The earth is 384,400 km from the moon.
• The earth is 152,000,000 km from the sun.
• The population of Delhi is about 2,50,00,000.

The post Large Numbers Around Us Class 7 Notes Maths Chapter 1 appeared first on Learn CBSE.

from Learn CBSE https://ift.tt/XLI8lZ2
via IFTTT