1. Large Numbers Around Us

Part I, printed Chapter 18 topics1 h

Chapter 1 of NCERT Mathematics for Class 7 (Part I, printed Chapter 1): Large Numbers Around Us. Four sections — Building a large number, Exact and approximate values, Patterns in products and Reasoning about the unimaginable. Eight videos, 1 h in all.

Worked answers to the 26 exercise questions in this chapter →

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Part 1

Building a large number

10 minWhat it actually takes to make one lakhTaste one variety of rice a day for a hundred years and you manage 36,500 — nowhere near a lakh. So three a day is hopeless too? It is not.10 min · 11 partsहिंदी9 minThe Land of Tens: each place is ten of the one beforeOur way of writing numbers is the cheapest possible recipe for building one. You can prove it by counting button presses.9 min · 11 partsहिंदी9 minCrores and millions: one number, two naming systemsA lakh is not a million and a crore is not a billion. The difference is not a table to memorise — it is where the commas fall.9 min · 11 partsहिंदी

Part 2

Exact and approximate values

9 minWhen an approximate answer is the better answerRounding is a judgement about consequences, not a rule about digits. Sweets get rounded up; medicine does not get rounded at all.9 min · 11 partsहिंदी10 minRounding to a nearest neighbour, and choosing which oneA number does not have a nearest round number. It has five, one for each place, and they do not all run the same way.10 min · 11 partsहिंदी

Part 3

Patterns in products

10 minFactorise and regroup instead of multiplying head-onThe multiplying-by-five shortcut is not about five. Our notation makes multiplying by ten free, and everything else follows from that.10 min · 11 partsहिंदी10 minPredicting how many digits a product will have, before multiplyingYou can say how many digits a product will have before you multiply. Checking examples and settling the question are different acts.10 min · 11 partsहिंदी

Part 4

Reasoning about the unimaginable

10 minAnswering "could this possibly fit?" by estimating in stagesCould this possibly fit? Two numbers and a comparison — and the number that decides it is usually the one nobody gave you.10 min · 11 partsहिंदी

What you will be able to do

  • Build 1,00,000 by stepping from the largest 3-digit number through the largest 5-digit number, adding one at each turn
  • Work out how many presses of a single fixed button are needed to reach a target, and say when the target cannot be reached at all
  • State how many zeros follow the 1 in a lakh, a crore, a million, a billion and an arab
  • Distinguish a quantity, which can sensibly be approximated, from a label, which cannot
  • Find the nearest thousand, ten thousand, lakh, ten lakh and crore of a given 8-digit number
  • Rewrite 5 as ten halved, 25 as a hundred quartered and 125 as a thousand divided by eight, and use each to compute a product in one line
  • Evaluate a short chain of patterned products and describe the pattern in the answers
  • Turn a "could it possibly fit" question into two quantities that can be compared

What this chapter assumes you already know

  • Reading and writing 4- and 5-digit numbers the Indian way, with a comma set after the thousands group
  • That each place in a written number is worth ten of the place to its right
  • Multiplication of a 3-digit number by a 3-digit number, and subtraction across five digits
  • The idea of "about" — that a measurement can be reported to the nearest thousand without being wrong
  • Multiplication and division by 10, 100 and 1000
  • Writing a number as a sum of multiples of place values, e.g. 321 as three hundreds, two tens and one unit
  • Reading an expression with brackets and evaluating it
  • Reading a 6-digit number aloud

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "A lakh is a large number, full stop."
  • "More digits means physically bigger."
  • "If one a day gets nowhere near a lakh in a lifetime, three a day won't either."
  • "75,000 is Chintamani's population."
  • "Commas are just decoration."
  • "A comparison proves the thing is big."
  • "There is one right way to make a number."
  • "The fewest presses is a rule you are told."