Another Peek Beyond the Point
Class 7 Mathematics · Ganita Prakash Part 2 · Chapter 4
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2- Mathematics
7- Mathematics
- Science
- + 3 more
- 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 decimal work to multiplication and division, treating decimals as the fractions they represent. To multiply two decimals, multiply the numbers as if there were no decimal points, then place the point so the number of decimal places in the product equals the sum of the decimal places in the factors — for example \(5.96 \times 24.8 = 147.808\). To divide by 10, 100, 1000, move the decimal point left by the number of zeros. Division uses the long-division (place-value) method: when ones are regrouped into tenths a decimal point is placed in the quotient, and regrouping continues into hundredths and thousandths. Some divisions never end, such as \(10 \div 3 = 3.333\dots\), revealing repeating decimals like \(1 \div 7 = 0.\overline{142857}\). When the divisor is itself a decimal, multiply both dividend and divisor by a power of 10 to make the divisor a whole number. The chapter ends with a fascinating real application: how leap-year rules (the \(0.2422\) extra days each year) keep our calendar aligned with the Earth's motion.