A Peek Beyond the Point
Class 7 Mathematics · Ganita Prakash Part 1 · Chapter 3
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- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Social Science
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Summary
This chapter extends the place value system below the units place to introduce decimals. To measure more precisely, a unit is split into ten one-tenths, each one-tenth into ten one-hundredths, and so on, so that \(1 = 10 \times \tfrac{1}{10}\) and \(\tfrac{1}{10} = 10 \times \tfrac{1}{100}\). A decimal point separates the whole-number part from the fractional part: \(70.5\) means \(7\times10 + 5\times\tfrac{1}{10}\), while \(7.05\) means \(7 + 5\times\tfrac{1}{100}\). You learn to read numbers like \(0.274\) as "zero point two seven four", to see that trailing zeros do not change a value \((0.2 = 0.20 = 0.200)\), and to locate and compare decimals on the number line by comparing digits place by place. The chapter connects decimals to everyday measurement — \(1\,\text{mm} = 0.1\,\text{cm}\), \(1\,\text{cm} = 0.01\,\text{m}\), \(1\,\text{g} = 0.001\,\text{kg}\), \(1\) paisa \(= \u20b90.01\) — and shows how to add and subtract decimals using the same column method as for whole numbers, plus a peek at the history of decimal notation.