Evaluate numerical expressions involving decimals

Key Notes:

Understanding Decimals

• A decimal represents a part of a whole number, positioned based on place values (tenths, hundredths, thousandths, etc.).
• Example: 0.5 means five-tenths, and 0.25 means twenty-five hundredths.

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Order of Operations (PEMDAS/BODMAS)

• Follow the correct sequence:
  P – Parentheses (Brackets)
  E – Exponents (Orders)
  MD – Multiplication and Division (left to right)
  AS – Addition and Subtraction (left to right)
• Example: (2.5 + 1.5) × 3 = 4 × 3 = 12

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Adding and Subtracting Decimals

• Align decimal points before performing the operation.
• Fill missing places with zeros for easy calculation.
• Example: 3.42 + 2.8 = 3.42 + 2.80 = 6.22

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Multiplying Decimals

• Ignore the decimal point and multiply as whole numbers.
• Count total decimal places in both numbers and adjust the final result accordingly.
• Example: 2.5 × 1.2 = 25 × 12 = 300, then place the decimal (2 places) → 3.00

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Dividing Decimals

• If the divisor is a decimal, shift the decimal point to make it a whole number and shift the dividend’s decimal point accordingly.
• Perform long division as usual.
• Example: 4.8 ÷ 1.2 = (48 ÷ 12) = 4

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Using Estimation for Accuracy

• Round decimals to the nearest whole number or significant place before solving to check if the answer is reasonable.
• Example: Estimate 3.89 × 1.2 ≈ 4 × 1 = 4

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Applying Decimals in Real-Life Problems

• Use decimal operations in money calculations, measurements, and scientific data.
• Example: A shirt costs $12.75, and you buy 3. Total cost = 12.75 × 3 = 38.25

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