Multiplying Decimals for 5th Grade: Rules and Examples

Multiplying decimals is used when we need to find a total from a rate (price per item × number of items), when computing area with decimal dimensions, and when scaling measurements. In Grade 5, students multiply decimals by whole numbers and by decimals, using the rule that the product has a number of decimal places equal to the total number of decimal places in the factors. This skill helps students calculate costs, find areas of rectangles with decimal sides, and solve real-world problems involving repeated addition or scaling.

The key insight is that we can multiply decimals as if they were whole numbers, then place the decimal point in the product by counting the total number of decimal places in the factors. For example, 1.25 × 4: multiply 125 × 4 = 500. The factor 1.25 has 2 decimal places; 4 has 0. So the product has 2 decimal places: 5.00. This rule works because multiplying by 0.1 shifts the decimal one place left; multiplying by 0.01 shifts it two places left; and so on.

DETAILED EXPLANATION

Steps to multiply decimals:

1. Ignore the decimal points and multiply the numbers as if they were whole numbers.

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2. Count the total number of decimal places in the factors.

3. Place the decimal point in the product so that it has the same total number of decimal places. Count from the right.

Example: 1.25 × 4. Multiply 125 × 4 = 500. Factors have 2 + 0 = 2 decimal places. So product: 5.00.

Example: 3.2 × 0.4. Multiply 32 × 4 = 128. Factors have 1 + 1 = 2 decimal places. So product: 1.28.

When multiplying by powers of 10 (10, 100, 1000), the decimal point moves right: 2.5 × 10 = 25; 2.5 × 100 = 250.

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

One apple costs $1.25. How much do 4 apples cost?

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Solutions:

Step 1: We need to multiply 1.25 × 4.

Step 2: Multiply as whole numbers, ignoring decimals: \(125 \times 4 = 500\).

Step 3: Count decimal places in the factors: 1.25 has 2 decimal places; 4 has 0. Total: 2 decimal places.

Step 4: Place the decimal point in the product so it has 2 decimal places. 500 → 5.00.

Step 5: Four apples cost $5.00.

Answer: $5.00

Example 2

Multiply 3.2 × 0.4

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Solutions:

Step 1: Multiply as whole numbers: \(32 \times 4 = 128\).

Step 2: Count decimal places: 3.2 has 1; 0.4 has 1. Total: 2 decimal places.

Step 3: Place the decimal point: 128 → 1.28.

Step 4: \(3.2 \times 0.4 = 1.28\).

Answer: 1.28

Example 3

A rectangle is 2.5 m by 1.6 m. Find the area.

Solutions:

Step 1: Area = length × width = \(2.5 \times 1.6\).

Step 2: Multiply as whole numbers: \(25 \times 16 = 400\).

Step 3: Count decimal places: 2.5 has 1; 1.6 has 1. Total: 2 decimal places.

Step 4: Place the decimal point: 400 → 4.00. The area is 4.0 square meters.

Answer: 4.0 square meters

Example 4

Multiply 0.12 × 0.5

Solutions:

Step 1: Multiply as whole numbers: \(12 \times 5 = 60\).

Step 2: Count decimal places: 0.12 has 2; 0.5 has 1. Total: 3 decimal places.

Step 3: Place the decimal point: 60 → 0.060, or 0.06 (we can drop trailing zeros after the decimal).

Answer: 0.06