Compare and order decimals

Key Notes:

1. Understanding Decimals

• Decimal Place Value: The position of a digit in a decimal number determines its value. Example:
  • Tenths: 0.1
  • Hundredths: 0.01
  • Thousandths: 0.001
• Reading Decimals: Read the number before the decimal point as a whole number and the digits after it as their place values.
  Example: 12.34 is “twelve and thirty-four hundredths.”

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2. Comparing Decimals

• Align Decimal Points: When comparing two or more decimals, align their decimal points vertically.
• Compare Digit by Digit: Start from the leftmost digit (whole number part) and move to the right (decimal part).
  • Example: Compare 0.456 and 0.453:
    • Tenths: Equal (4=4)
    • Hundredths: Equal (5=5)
    • Thousandths: 6>3, so 0.456>0.453.

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3. Ordering Decimals

• Ascending Order: Arrange decimals from the smallest to the largest.
  • Example: 0.3,0.25,0.305:
    • 0.25<0.3<0.305
• Descending Order: Arrange decimals from the largest to the smallest.
  • Example: 0.45,0.78,0.67:
    • 0.78>0.67>0.45

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4. Using Zeroes for Consistency

• Add trailing zeros to decimals to make them easier to compare without changing their value.
  Example: Compare 0.3 and 0.300:
  • Align as 0.300 and 0.300. Both are equal.

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5. Applications in Real Life

• Decimals are used in:
  • Money (e.g., 5.75 dollars).
  • Measurements (e.g., 2.45 meters).
  • Weight (e.g., 3.2 kg).

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6. Practice Problems

1. Compare 3.14 and 3.141.
   Answer: 3.141>3.14
2. Order 0.25,0.245,0.30 in ascending order.
   Answer: 0.245<0.25<0.3

Learn with an example

Try some practice problems!