Understanding Decimals

Reading Decimals

• A decimal is a way to represent a fraction using a point (.) instead of a line (/)
• The point is called the decimal point
• The digits to the left of the decimal point are whole numbers
• The digits to the right of the decimal point are fractional parts
• Examples:
  • 4.5 (four and five tenths)
  • 2.75 (two and seventy-five hundredths)

Writing Decimals

• To write a decimal, divide the numerator (top number) by the denominator (bottom number)
• Examples:
  • 3/4 = 0.75 (three divided by four)
  • 2/5 = 0.4 (two divided by five)
• Decimals can be written in word form:
  • 0.5 = five tenths
  • 0.25 = twenty-five hundredths

Comparing Decimals

• To compare decimals, compare the digits to the right of the decimal point
• Compare the digits from left to right, starting with the tenths place
• Examples:
  • 0.4 > 0.3 (four tenths is greater than three tenths)
  • 0.75 = 0.75 (equal)

Ordering Decimals

• To order decimals, arrange them from least to greatest or greatest to least
• Compare the digits to the right of the decimal point, starting with the tenths place
• Examples:
  • Order from least to greatest: 0.3, 0.4, 0.5
  • Order from greatest to least: 0.5, 0.4, 0.3

Decimal Operations

• Addition and Subtraction:
  • Add or subtract the decimals as you would with whole numbers
  • Align the decimal points
  • Examples:
    • 2.5 + 1.8 = 4.3
    • 4.5 - 2.2 = 2.3
• Multiplication:
  • Multiply the decimals as you would with whole numbers
  • Multiply the decimal parts separately
  • Examples:
    • 2.5 × 3.4 = 8.5
    • 0.5 × 0.2 = 0.1
• Division:
  • Divide the decimals as you would with whole numbers
  • Divide the decimal parts separately
  • Examples:
    • 4.5 ÷ 2.5 = 1.8
    • 0.6 ÷ 0.3 = 2

Representing Decimals

• A decimal is a way to represent a fraction using a point (.) instead of a line (/)
• The point is called the decimal point
• Digits to the left of the decimal point are whole numbers
• Digits to the right of the decimal point are fractional parts

Examples of Decimals

• 4.5 represents four and five tenths
• 2.75 represents two and seventy-five hundredths

Writing Decimals from Fractions

• Divide the numerator (top number) by the denominator (bottom number) to write a decimal
• Examples:
  • 3/4 = 0.75 (three divided by four)
  • 2/5 = 0.4 (two divided by five)

Writing Decimals in Word Form

• Decimals can be written in word form
• Examples:
  • 0.5 = five tenths
  • 0.25 = twenty-five hundredths

Comparing Decimals

• Compare decimals by comparing the digits to the right of the decimal point
• Compare digits from left to right, starting with the tenths place
• Examples:
  • 0.4 > 0.3 (four tenths is greater than three tenths)
  • 0.75 = 0.75 (equal)

Ordering Decimals

• Arrange decimals from least to greatest or greatest to least
• Compare digits to the right of the decimal point, starting with the tenths place
• Examples:
  • Order from least to greatest: 0.3, 0.4, 0.5
  • Order from greatest to least: 0.5, 0.4, 0.3

Decimal Operations

Addition and Subtraction

• Add or subtract decimals as you would with whole numbers
• Align the decimal points
• Examples:
  • 2.5 + 1.8 = 4.3
  • 4.5 - 2.2 = 2.3

Multiplication

• Multiply decimals as you would with whole numbers
• Multiply the decimal parts separately
• Examples:
  • 2.5 × 3.4 = 8.5
  • 0.5 × 0.2 = 0.1

Division

• Divide decimals as you would with whole numbers
• Divide the decimal parts separately
• Examples:
  • 4.5 ÷ 2.5 = 1.8
  • 0.6 ÷ 0.3 = 2