Another Peek | Class 7 Mathematics Notes

4.3 Decimal Division

Decimal division extends the concept of division of whole numbers to decimals. The chapter explains division using place value (long division) to find decimal quotients. When dividing by numbers like 10, 100, 1000, the decimal point moves to the left by the number of zeros in the divisor. For example, 3.9 ÷ 10 = 0.39 and 3.9 ÷ 100 = 0.039. For division by numbers not powers of 10, the method involves converting the divisor into a whole number by multiplying numerator and denominator by the same power of 10, then performing long division. The chapter illustrates division with decimal quotients through examples like 1325 ÷ 4 = 331.25 and 237 ÷ 8 = 29.625 using regrouping of place values (thousands, hundreds, tens, ones, tenths, hundredths, thousandths). It emphasizes placing the decimal point in the quotient when regrouping ones into tenths. The section also covers division with decimal dividends and decimal divisors, showing how to convert decimals to fractions and perform multiplication by reciprocals. The chapter discusses cases where division results in repeating decimals, such as 10 ÷ 3 = 3.333..., and introduces cyclic numbers like 142857 arising from 1 ÷ 7. It concludes by exploring the relationship between dividend, divisor, and quotient, noting that the quotient may be greater or less than the dividend depending on the divisor's value.

📊 Diagram: Stepwise diagrams illustrating long division of numbers like 1324 ÷ 4 and 237 ÷ 8 showing regrouping of thousands, hundreds, tens, ones, tenths, hundredths, and thousandths, with decimal point placement in quotient.

🧪 Activity: Exercises on converting fractions to decimals, performing decimal division by converting divisors to whole numbers, and exploring repeating decimals.

🔗 Connection: This section builds on decimal multiplication and prepares students to understand real-life applications of decimals and the behavior of decimal expansions, leading to the next section on calendar calculations.