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Grade 8/ Mathematics/ A Story of Numbers
Chapter 3 · NCERT Class 8 Ganita Prakash

A Story of Numbers

Ten digits and one clever idea — place value — can write any number ever needed, from a bus fare to the national budget. It took civilisations centuries, and a symbol for zero, to get here. Tap each idea to follow the story.

📐 3 topics⏱ ~25 min📝 12-question quiz
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The six ideas behind our numbers

Writing numbers looks obvious now, but every part of it was an invention. Tap each term to see what it means and why it matters.

Explore · Numbers & place valuetap a term

Learn

The three big ideas

  • The same digit means different amounts depending on where it sits. In 4,04,040 the three 4s mean 4 lakh, 4 thousand and 4 tens.
  • Base ten: each place is ten times the place to its right — ones, tens, hundreds, thousands, and so on.
  • Expanded form shows this clearly: 3,605 = 3×1000 + 6×100 + 0×10 + 5×1.
  • Only ten digits (0–9) are needed to write any number, however large.

Worked example. Write 9,07,06,005 in expanded form.

1. Name the places from the right: ones, tens, hundreds, thousands, ten-thousands, lakhs, ten-lakhs, crores.

2. Multiply each non-zero digit by its place: 9 crore, 7 lakh, 6 thousand, 5 ones.

3. 9,07,06,005 = 9×1,00,00,000 + 7×1,00,000 + 6×1,000 + 5×1.

  • Indian system — places run ones, tens, hundreds, thousands, ten-thousands, lakhs, ten-lakhs, crores. Commas come after the first 3 digits, then every 2: 1,23,45,678.
  • International system — places run thousands, millions, billions. Commas come every 3 digits: 12,345,678.
  • Quick conversions: 10 lakh = 1 million, 1 crore = 10 million, 1 billion = 100 crore.

Worked example. A figure is written as 6 crore. Convert it to the International system.

1. 1 crore = 10 million.

2. So 6 crore = 6 × 10 million = 60 million (written 60,000,000).

Common mistake: treating a million as the same as a crore. A million is only 10 lakh — a crore is ten times bigger.
  • Early counting used tally marks and symbols. Different civilisations built their own numerals.
  • Roman numerals (I, V, X, L, C, D, M) had no zero and no place value, which made adding and multiplying slow and awkward.
  • The numerals we use today grew from numerals developed in India (Brahmi numerals onward), where the idea of place value plus a symbol for zero (shunya) came together.
  • These travelled through Arab scholars to Europe — which is why they are often called Hindu–Arabic numerals. Zero made place value, and easy arithmetic, possible.

Where you'll meet it

Big numbers in real life

Census & population

Indian newspapers report populations in lakhs and crores. Reading "85 lakh" or "1.4 crore" correctly — and converting to millions for a global report — is everyday place-value work.

Budgets and money

Government and company budgets run into lakhs and crores of rupees. Placing the commas right is what keeps ₹5,00,000 from being misread as ₹50,000.

Reading world data

Global science and business reports use millions and billions. Knowing 1 crore = 10 million lets you compare an Indian figure with an international one without mistakes.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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Interactive built to the OpenMAIC approach (THU-MAIC, MIT). Content from the NCERT Class 8 Ganita Prakash textbook (ncert.nic.in).

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