NCERT Solutions Ganita Prakash (Part 1) Chapter 1 –181.5 Patterns in Products — Fascinating Facts about Large Numbers

Book page 16 Updated on2026-09-05

Q1.
1250 × 380 = ______________ is the number of kīrtanas composed by Purandaradāsa according to legends. How many years did he live to compose so many songs? At what age did he start composing songs? If he composed 4,75,000 songs, how many songs per year did he have to compose?
Answer

The hidden number is 4,75,000.

1250 × 380
= 1250 × 38 × 10
= 47,500 × 10
= 4,75,000

Indian system: four lakh seventy five thousand
American system: four hundred seventy five thousand

How many songs per year? Purandaradāsa is said to have lived about 80 years (1484–1564).

If he composed for all 80 years:
4,75,000 ÷ 80 = about 5,938 songs a year
= about 16 songs every single day

If he began at about age 30 and composed for 50 years:
4,75,000 ÷ 50 = 9,500 songs a year
= about 26 songs every day
Why it happens: Working out the rate is what shows how astonishing the legend is — 16 complete songs a day, every day, for eighty years. Most historians therefore treat 4,75,000 as a traditional figure rather than an exact count; a few hundred of his kīrtanas survive today.
Did you know? Purandaradāsa, a 15th-century composer and singer, is called the Pitāmaha (grandfather) of Carnatic music. The graded lessons he designed are still the first thing a Carnatic student learns.
Q2.
2100 × 70,000 = _______________ is the approximate distance in kilometers, between the Earth and the Sun.
Answer

The hidden number is 14,70,00,000 km — about 14 crore 70 lakh kilometres.

2100 × 70,000
= 21 × 7 × 100 × 10,000
= 147 × 10,00,000
= 14,70,00,000

Indian system: fourteen crore seventy lakh
American system: one hundred forty seven million
Why it happens: Strip off the zeroes first — 21 × 7 = 147 — then put back the 2 + 4 = 6 zeroes you removed. This is far quicker than long multiplication.
Did you know? The book adds that the farthest distance is about 152 million km, i.e. 15,20,00,000 km. The Earth's orbit is slightly oval, so the distance changes through the year.
Q3.
6400 × 62,500 = _________________ is the average number of litres of water the Amazon river discharges into the Atlantic Ocean every second.
Answer

The hidden number is 40,00,00,000 litres every second — 40 crore litres.

6400 × 62,500
= 64 × 625 × 100 × 100
= 40,000 × 10,000
= 40,00,00,000

Indian system: forty crore
American system: four hundred million
Why it happens: 64 × 625 is worth spotting: 625 = 10,000 ÷ 16, so 64 × 625 = 64 ÷ 16 × 10,000 = 4 × 10,000 = 40,000. Regrouping again saves all the long multiplication.
Did you know? So much fresh water pours out that drinkable water is found 160 km out into the open sea. In one second the Amazon delivers enough water to fill about 160 Olympic swimming pools.
Q4.
13,95,000 ÷ 150 = _________________ is the distance (in kms) of the longest single-train journey in the world.
Answer

The hidden number is 9,300 km.

13,95,000 ÷ 150
= 13,95,000 ÷ 15 ÷ 10
= 93,000 ÷ 10
= 9,300

Both systems: nine thousand three hundred
Why it happens: Splitting 150 into 15 × 10 makes the division easy — 1395 ÷ 15 = 93, so 13,95,000 ÷ 15 = 93,000, and one more division by 10 gives 9,300.
Did you know? That is the Moscow–Vladivostok run on the Trans-Siberian railway, taking about 7 days. India's longest route, Dibrugarh (Assam) to Kanyakumari (Tamil Nadu), covers 4,219 km in about 76 hours — a little under half the Russian distance.
Q5.
Adult blue whales can weigh more than 10,50,00,000 ÷ 700 = _________________ kilograms.
Answer

The hidden number is 1,50,000 kg — one lakh fifty thousand kilograms, or 150 tonnes.

10,50,00,000 ÷ 700
= 10,50,00,000 ÷ 7 ÷ 100
= 1,50,00,000 ÷ 100
= 1,50,000

Indian system: one lakh fifty thousand
American system: one hundred fifty thousand
Why it happens: Cancel the zeroes first. 10,50,00,000 ÷ 100 = 10,50,000, and 10,50,000 ÷ 7 = 1,50,000. Dividing in two easy stages beats one long division.
Did you know? A newborn blue whale already weighs about 2,700 kg — as much as an adult hippopotamus. Its heart alone is about 700 kg, and it eats up to 3,500 kg of krill a day. Even Argentinosaurus, the largest known land animal, is estimated at only 90,000 kg.
Q6.
52,00,00,00,000 ÷ 130 = _________________ was the weight, in tonnes, of global plastic waste generated in the year 2021.
Answer

The hidden number is 40,00,00,000 tonnes — 40 crore tonnes.

52,00,00,00,000 ÷ 130
= 52,00,00,00,000 ÷ 13 ÷ 10
= 4,00,00,00,000 ÷ 10
= 40,00,00,000

Indian system: forty crore
American system: four hundred million
Why it happens: 52 ÷ 13 = 4 exactly, so the whole division collapses to moving the decimal — no long division needed at all.
Large number fact: A single gram of healthy soil can hold 10 crore to 1 arab (100 million to 1 billion) bacteria and 1 lakh to 10 lakh fungi. Share such large-number facts with your class.
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