Maths micro teaching copy
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This document provides examples of converting recurring decimals to fractions in the form of p/q. It gives step-by-step solutions for converting decimals like 0.32222..., 0.12333..., 0.111..., 0.6666..., and 0.001... to their equivalent fractions 29/90, 111/900, 1/9, 2/3, and 1/999 respectively. The process involves letting the decimal equal a variable x, multiplying both sides by a power of 10, subtracting the resulting equations to isolate x, and then rationalizing the fraction.
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- 1. Micro –Teaching Session { Mathematics }
- 2. Conversion in the form of p/q Chapter-1 Number Systems
- 3. What is a Rational Number? A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0.
- 4. Conversion of a Mixed Recurring Decimal in the Form of p/q:- • Examples:- • Express the following decimal in the form of p/q:- • A) 0.32222......{BAR ON 2} • Sol:-Let x be = 0.322222......(Eq-1) ∴ Multiplying Both sides by 10. • 10x = 3.2222.......(Eq-2) • Subtracting (Eq-2) - (Eq-1) • 10x – x = 3.2222.... - 0.32222..... • 9x = 2.9 • X = 2.9/9 • X= 29/90 { By removing the decimal }
- 5. • Examples:- • Express the following decimal in the form of p/q:- • B) 0.12333......{BAR ON 3} • Sol:-Let x be 0.123333......(Eq-1) • ∴ Multiplying Both sides by 10. • 10x = 1.2333.......(Eq-2) • Subtracting (Eq-2) - (Eq-1) • 10x – x = .... - 1.2333..... - 0.12333...... • 9x = 1.11 • X = 1.11/9 • X= 111/900 { By removing the decimal }
- 6. • Examples:- • Express the following decimal in the form of p/q:- • C) 0.111.....{BAR ON 1} • Sol:-Let x be = 0.11111.....(Eq-1) • ∴ Multiplying Both sides by 10. • 10x = 1.1111.......(Eq-2) • Subtracting (Eq-2) - (Eq-1) • 10x – x = 1.1111... - 0.11111..... • 9x = 1 • X = 1/9
- 7. • Examples:- • Express the following decimal in the form of p/q:- • D) 0.6666......{BAR ON 6} • Sol:-Let x be = 0.666666.....(Eq-1) • ∴ Multiplying Both sides by 10. • 10x = 6.66666.......(Eq-2) • Subtracting (Eq-2) - (Eq-1) • 10x – x = 6.66666... - 0.66666..... • 9x = 6 • X = 2/3
- 8. • Examples:- • Express the following decimal in the form of p/q:- • E) 0.001 {BAR ON 001} • Sol:-Let X be = 0.001.....(Eq-1) • ∴ Multiplying Both sides by1000. • 1000x = 001.001001001.......(Eq-2) • Subtracting (Eq-2) - (Eq-1) • 1000x – x = 001.001001.... - 0.001001001..... • 999x = 1 • X = 1/999
- 10. Thank you