Compare and order decimals

Key Notes:

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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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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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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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.

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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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!