Large Numbers Around Us Class 7 Notes Maths Chapter 1

Class 7 Maths Chapter 1 Notes Large Numbers Around Us

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

→ 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?”

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.”

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.

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.

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).

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.

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.

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.

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.

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.

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.

Class 7 Maths Notes

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