6. Division of decimal numbers

Multiplication of Decimal Numbers 
    Multiplication of a decimal numbers by 10 or its factors 
    Rule: Shift the decimal point to the right place equivalent to numbers of zeros followed by 1.
    For example, 5.23 x10 = 52.3 
    13.438 x 100 = 1343.8 (since in 100 one is followed by 2 zeroes hence the decimal point is shifted to two places to the right)
    Multiplication of a decimal by a whole number or by decimal number .
    Rule: Multiply the decimal numbers by the whole number or another decimal number as per rules of multiplication.
    Rule: Place the decimal in the result at such a place from the left most digit, which is equal to the sum of the places from the left, of the decimal number or whole number and the decimal number which is multiplied.

Illustration 1
        Multiply : 0.534 by 2
Solution    
        The product must contain 3 places of decimal hence 0.534 x 2 = 1.068.

Illustration 2
        Multiply : 2.054 x 4.32
Solution
        Multiply : 2.054 and 4.32 without putting decimal i.e. 2054 x 432 = 887328
        The product must contain 3 + 2 = 5 decimal places. Since sum of the decimal places of the two
        numbers = 5 hence 2.054 x 4.32 = 8.87328

Illustration 3
        Multiply : 2 × 0.2 × 0.002
Solution
        2 × 2 × 2 = 8
        Sum of the decimal places of the given numbers = 4 hence the product must contain 4 places of decimals
        So 2 × 0.02 × 0.002 = 0.0008