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Here are some tips for Decimal Multiplication, which aligns with New York state standards:

Decimal Multiplication

Steps for decimal multiplication:

1. Ignore the decimal points for now, and multiply as whole numbers.
2. Add the number of digits to the right of the decimal point for each decimal.
3. Place the decimal point in the answer.

Example 1:

Multiply: 3.2 × 0.4
Ignore the decimal points and multiply.

    32
  × 04
   128

Figure out where to place the decimal point.

    3.2   ← 1 digit to the right of the decimal point
  × 0.4   ← 1 digit to the right of the decimal point

Place the decimal point in the answer.

    3.2
  × 0.4
   1.28   ← 2 (1 + 1) digits to the right of the decimal point

3.2 × 0.4 = 1.28

Example 2: Adding zeros to place the decimal point

Multiply: 0.08 × 0.1
Ignore the decimal points and multiply.

    8
  × 1
    8

Figure out where to place the decimal point.

    0.08   ← 2 digits to the right of the decimal point
   × 0.1   ← 1 digit to the right of the decimal point

Place the decimal point in the answer.

    0.08
   × 0.1
   0.008   ← 3 (2 + 1) digits to the right of the decimal point
           Add zeros when there are no more digits to the right.

0.08 × 0.1 = 0.008

Example 3: Remember the zeros!

Multiply: 0.35 × 1.6
Ignore the decimal points and multiply.

   35
 × 16
  210
  35 
  560

Figure out where to place the decimal point.

  0.35   ← 2 digits to the right of the decimal point
 × 1.6   ← 1 digit to the right of the decimal point

Place the decimal point in the answer.

  0.35
 × 1.6
 0.560   ← 3 (2 + 1) digits to the right of the decimal point
         Remember to count the first zero when placing the decimal!

0.35 × 1.6 = 0.56

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