Multiplying Decimals
Learn how to multiply decimal numbers using place value strategies and the standard algorithm.
Definition
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Worked Examples
Calculate
Multiply as whole numbers
→ 1300
Count decimal places in factors
has 2 decimal places; has 0 → Total: 2 places
Place the decimal point
Move 2 places from the right: →
Answer:
Common Mistakes
Forgetting to count decimal places in both numbers
Why it's wrong: Students sometimes only count the decimal places in one factor, leading to an answer that's 10 times too big or small.
Correct: Always count decimal places in BOTH factors, then add them together.
Placing the decimal point from the left instead of the right
Why it's wrong: The rule is to count from the right side of the product, not from the left.
Correct: Count decimal places from the RIGHT side of your answer.
Thinking is wrong because the answer is smaller
Why it's wrong: When multiplying by a number less than 1, the product is smaller than the original. This is correct!
Correct: Multiplying by a decimal less than 1 gives a smaller answer. is correct.
Dropping leading zeros
Why it's wrong: When the product needs more decimal places than digits, students forget to add zeros.
Correct: If and you need 4 decimal places, the answer is
Interactive Visual
Place Value Chart
| Ones 1 | Tenths 0.1 | Hundredths 0.01 |
|---|---|---|
| 2 | 4 | 5 |
Expanded Form:
2 × 1 + 4 × 0.1 + 5 × 0.01
Click on any place value to highlight it and see its value.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
15 problemsWhat is ?
Why It Matters
- Shopping: Calculating the cost of 2.5 kg of fruit at 3.20 dollars per kg
- Cooking: Scaling a recipe by 1.5 to serve more people
- Science: Calculating area with precise measurements (2.4 m × 3.5 m)
- Money: Figuring out sales tax (85.50 dollars × 0.08)
Real World Applications
Shopping and Sales Tax
Every purchase involves decimal multiplication when calculating tax or discounts.
Example:
If sales tax is 8% (0.08), the tax on a 45.00 dollar item is dollars.
You're buying a jacket that costs 65.50 dollars. The sales tax rate is 0.07 (7%).
How much tax will you pay?
Step 1: Write the mathematical expression
Calculate:
Cooking and Recipes
Scaling recipes up or down requires multiplying ingredient amounts by decimals.
Example:
A recipe calls for 2.5 cups of flour. To make 1.5 times the recipe: cups.
A smoothie recipe needs 0.75 cups of yogurt. You want to make 2.5 servings.
How much yogurt do you need?
Step 1: Write the mathematical expression
Calculate:
Area Calculations
Finding the area of rectangles often involves decimal measurements.
Example:
A garden bed is 3.5 meters by 2.4 meters. Area = square meters.
A poster is 0.6 meters wide and 0.8 meters tall.
What is the area of the poster in square meters?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1Multiply decimals like whole numbers, ignoring the decimal points at first
- 2Count the total decimal places in BOTH factors
- 3Place the decimal point that many places from the RIGHT in your answer
- 4Add zeros to the left if needed (e.g., )
- 5Multiplying by a decimal less than 1 gives a smaller answer
Frequently Asked Questions
Glossary
- Factor
- A number being multiplied. In , both 3.5 and 2 are factors.
- Product
- The result of multiplication. In , the product is 7.
- Decimal place
- The position of a digit to the right of the decimal point. In , there are 2 decimal places.
- Leading zero
- A zero that appears before other digits, like the 0 in .