Step 1: Look at the digit in the tenths place (first digit after the decimal point)

Step 2: If the tenths digit is 5 or greater → Round UP (add 1 to ones place)

Step 3: If the tenths digit is less than 5 → Round DOWN (keep ones place same)

Step 4: Multiply the rounded whole numbers

Estimate: 6.75 × 8.56

• 6.75 → 7 is greater than 5, so round UP to 7

• 8.56 → 5 equals 5, so round UP to 9

• 7 × 9 = 63

Estimated Product ≈ 63

Step 1: Use a 10 × 10 grid (100 small squares)

Step 2: Shade COLUMNS (vertical) for the first decimal

Step 3: Shade ROWS (horizontal) for the second decimal

Step 4: Count the DOUBLE-SHADED squares (overlap)

Step 5: Double-shaded squares = answer in hundredths

Multiply: 0.4 × 0.6

• Shade 4 columns (for 0.4 or 4 tenths)

• Shade 6 rows (for 0.6 or 6 tenths)

• Double-shaded area = 24 squares

• 24 out of 100 = 24/100 = 0.24

Product = 0.24

• Use multiple grids if decimal is greater than 1.0

• Each complete grid = 1.0

• Shade columns for one factor

• Shade rows for the other factor

• Count ALL double-shaded squares across all grids

Multiply: 1.2 × 0.5

• Use 2 grids (since 1.2 > 1)

• Shade columns: 1 full grid + 2 columns in next grid

• Shade 5 rows across both grids

• Total double-shaded = 60 squares

Product = 0.60 or 0.6

The number of decimal places in the PRODUCT equals the TOTAL number of decimal places in ALL the factors.

Step 1: Ignore the decimal points and multiply as whole numbers

Step 2: Count decimal places in the first factor

Step 3: Count decimal places in the second factor

Step 4: Add the decimal places from both factors

Step 5: Place decimal point in product from RIGHT to LEFT by that many places

Example 1: 3.2 × 1.5

• Multiply without decimals: 32 × 15 = 480

• 3.2 has 1 decimal place

• 1.5 has 1 decimal place

• Total = 1 + 1 = 2 decimal places

• Place decimal in 480 → 4.80 = 4.8

Example 2: 0.7 × 0.352

• Multiply: 7 × 352 = 2464

• 0.7 has 1 decimal place

• 0.352 has 3 decimal places

• Total = 1 + 3 = 4 decimal places

• Place decimal in 2464 → 0.2464

If the product has fewer digits than decimal places needed, add zeros on the left before placing the decimal point.

Step 1: Break each decimal into place value parts (ones, tenths, hundredths)

Step 2: Draw a rectangle and divide it based on place values

Step 3: Multiply each section (length × width of each part)

Step 4: Add all the partial products

Step 5: The sum = final product

Multiply: 2.3 × 1.5

Break down:

• 2.3 = 2 + 0.3

• 1.5 = 1 + 0.5

Area Model Sections:

Add all parts:

2.0 + 1.0 + 0.3 + 0.15 = 3.45

Product = 3.45

Step 1: Multiply without decimal points

Step 2: Count total decimal places in both factors

Step 3: Place decimal in product (max 2 places)

Step 4: Add zeros on left if needed

Example 1: 0.5 × 0.8

• 5 × 8 = 40

• Total decimal places: 1 + 1 = 2

• Product = 0.40 = 0.4

Example 2: 1.2 × 0.45

• 12 × 45 = 540

• Total decimal places: 1 + 2 = 3

• But wait! Product can have up to 3 decimal places

• Product = 0.540 = 0.54 (2 decimal places after removing trailing zero)

Example 1: 0.25 × 0.34

• 25 × 34 = 850

• Total decimal places: 2 + 2 = 4

• Product = 0.0850 = 0.085 (3 decimal places)

Example 2: 1.5 × 0.125

• 15 × 125 = 1875

• Total decimal places: 1 + 3 = 4

• Product = 0.1875

• Note: This has 4 decimal places, but remove trailing zeros for final answer

If product has fewer digits than decimal places needed, add zeros to the LEFT of the number before placing the decimal point.

> = Greater than

< = Less than

= = Equal to

Step 1: Calculate both products

Step 2: Compare the decimal numbers place by place

Step 3: Start from the leftmost digit (ones, then tenths, then hundredths)

Step 4: Use the appropriate comparison symbol

Compare: 0.5 × 0.6 ⃝ 0.4 × 0.7

Calculate Left Side:

0.5 × 0.6 = 0.30 = 0.3

Calculate Right Side:

0.4 × 0.7 = 0.28

Compare:

0.30 vs 0.28

Compare tenths: 3 > 2

Answer: 0.5 × 0.6 > 0.4 × 0.7

Compare place by place from LEFT to RIGHT:

① Ones place

② Tenths place (0.1)

③ Hundredths place (0.01)

④ Thousandths place (0.001)

Compare: 0.25 × 0.15 ⃝ 0.12 × 0.32

Calculate Left Side:

0.25 × 0.15

25 × 15 = 375

Decimal places: 2 + 2 = 4

Product = 0.0375

Calculate Right Side:

0.12 × 0.32

12 × 32 = 384

Decimal places: 2 + 2 = 4

Product = 0.0384

Compare:

0.0375 vs 0.0384

Ones place: 0 = 0 ✓

Tenths: 0 = 0 ✓

Hundredths: 3 = 3 ✓

Thousandths: 7 < 8 ✓

Answer: 0.25 × 0.15 < 0.12 × 0.32

✓ Always count decimal places in BOTH numbers before placing the decimal in your answer

✓ Don't forget to add zeros on the left if your product has fewer digits than needed

✓ Remove trailing zeros after the decimal point (0.50 = 0.5)

✓ Keep all zeros in the product BEFORE placing the decimal point

✓ When using grids, columns = one factor, rows = other factor

✓ When using area models, break numbers by place value first

✓ For estimation, round to nearest whole number, then multiply