Decimals

• Introduction

  • Need for Decimals
  • Extension of place value system from fractions
  • Real-life uses (Money, Length, Weight)

• Place Value Table for Decimals

  • Whole number part (Left of decimal point)
    • Ones, Tens, Hundreds, etc.
  • Decimal point (.)
  • Decimal part (Right of decimal point)
    • Tenths ($\frac{1}{10}$ or $0.1$)
    • Hundredths ($\frac{1}{100}$ or $0.01$)
    • Thousandths ($\frac{1}{1000}$ or $0.001$)

• Fractions and Decimals

  • Converting Fractions to Decimals
    • Denominators as powers of 10 (10, 100, 1000)
  • Converting Decimals to Fractions
    • Removing decimal point and placing 10, 100, etc., in denominator
    • Reducing to simplest form

• Comparing Decimals

  • Step 1: Compare whole number parts
  • Step 2: If whole parts are equal, compare tenths digit
  • Step 3: Compare hundredths, then thousandths if necessary
  • Example: $3.45 > 3.42$

• Using Decimals in Daily Life

  • Money
    • 100 paise = ₹ 1
    • 1 paisa = ₹ $\frac{1}{100}$ = ₹ $0.01$
  • Length
    • 10 mm = 1 cm $\Rightarrow$ 1 mm = $\frac{1}{10}$ cm = $0.1$ cm
    • 100 cm = 1 m $\Rightarrow$ 1 cm = $\frac{1}{100}$ m = $0.01$ m
    • 1000 m = 1 km $\Rightarrow$ 1 m = $\frac{1}{1000}$ km = $0.001$ km
  • Weight (Mass)
    • 1000 g = 1 kg $\Rightarrow$ 1 g = $\frac{1}{1000}$ kg = $0.001$ kg

• Operations on Decimals

  • Addition of Decimals
    • Align decimal points vertically
    • Add like whole numbers
  • Subtraction of Decimals
    • Align decimal points vertically
    • Pad with zeros if necessary
    • Subtract like whole numbers