Class 7 Maths Chapter 1: Large Numbers Around Us Notes

What is this chapter about?

The chapter opens in a market in Chintamani, a town in Karnataka. A farmer hears that India once grew about a lakh varieties of rice, and his son wonders whether anyone could taste them all in a lifetime. Eating one variety a day for 100 years gives only 36,500 days, far short of a lakh. Questions like this run through the whole chapter: how big is a lakh, or a crore, and how do we read, write, round and calculate with such numbers?

How big is one lakh?

Add 1 to 999 and you get 1,000, the smallest 4-digit number. Add 1 to 99,999 and you get 1,00,000, the smallest 6-digit number, read as one lakh. It has 5 zeros.

Is a lakh big? It depends on what you compare it with. A lakh days is about 274 years, but one stadium in Ahmedabad seats more than a lakh people. Large measures also make more sense next to something familiar: Somu is 1 m tall, a floor of his building is about 4 m, and the 10-floor building is about 40 m. The Statue of Unity, about 180 m, is roughly four and a half such buildings.

Land of Tens: place value with button clicks

In the Land of Tens, calculators have only some keys. A calculator with only a +1000 key needs 100 presses to show a lakh; one with +100 needs 1,000, and one with +10 needs 10,000. A calculator with all the keys (+1, +10, +100 and so on) can make 5072 in many ways, but the fewest clicks are 5 on +1000, 7 on +10 and 2 on +1: 14 clicks, the sum of the digits. The fewest clicks always follow place value.

Crores, arabs, millions and billions

Press +10,00,000 ten times and you get 100 lakh, called a crore: 1,00,00,000, with 7 zeros. A hundred crore make an arab. In the Indian system commas go after three digits from the right and then after every two (3-2-2-2). The American, or International, system uses millions and billions, with a comma after every three digits. So 10 lakh is 1 million, 1 crore is 10 million and 100 crore is 1 billion. The words lakh and crore come from Sanskrit. Read more in lakhs and crores.

Exact and approximate values

Often an exact number is not needed. Chintamani’s 2011 population was 76,068, but “about 75,000” gives the idea. We round up when a bigger figure is safer, as when a school of 732 people orders 750 sweets, and round down when a smaller figure suits, as when a ₹470 item is said to cost about ₹450. Exact numbers are still needed for phone numbers and money in a bank.

Large numbers also have nearest neighbours: the nearest thousand, ten thousand, lakh, ten lakh and crore. Estimating first helps too: 4,63,128 + 4,19,682 must be between 8,50,000 and 8,83,128. The chapter then asks questions about the populations of 20 cities in 2001 and 2011. See rounding and estimation.

Patterns in products

Multiplying by 5 is the same as halving and then multiplying by 10, so 116 × 5 = 58 × 10 = 580. In the same way, × 25 is ÷ 4 and × 100, and × 125 is ÷ 8 and × 1000. Grouping factors into round numbers helps too: 125 × 40 × 8 × 25 = 1000 × 1000. The chapter also asks how many digits a product has; two 2-digit numbers always give 3 or 4 digits. Then a few multiplications and divisions uncover facts, such as the distance to the Sun (about 14,70,00,000 km) and the weight of a blue whale. Read patterns in products.

Did you ever wonder…?

The last section plays with large numbers. Could Mumbai, with more than 1 crore 24 lakh people, fit into 1 lakh buses of 50 seats? No: they hold only 50 lakh. Could you reach the Moon at 100 km a day in 10 years? Work in stages: 36,500 km a year, 3,65,000 km in 10 years, still 19,400 km short.

The chapter closes with a puzzle about digits made of toothpicks. Answers to every question, the Figure it Out exercises and the puzzle are in the NCERT solutions for Chapter 1.