Multiplication & Dividing a decimal by a whole number

Multiplication of a decimal by another decimal: 
To multiply a decimal by another decimal, we follow following steps :
Step I     Multiply the two decimals without decimal point just like whole numbers.
Step II     Insert the decimal point in the product by counting as many places from the right to left as the sum of the number of decimal places of the given decimals.

Ex.1    Find the product of 9.2 and 6.07.
Sol.    We have,
        
     ∴      92 × 607 = 55844
Since the sum of the decimal places in the given decimals is 1 + 2 = 3.
So, the product must contain 3 places of decimals. Hence 9.2 × 6.07 = 55.844 

Ex.2    Multiply 0.0345 by 0.0237
Sol.    We have,

  ∴  345 × 237 = 81765
We observe that the sum of the decimals in the given decimals is 4 + 4 = 8
So, the product must contain 8 places of decimals.
Hence, 0.0345 × 0.0237 = 0.00081765

Dividing  a decimal by a whole number    
A decimal can be divided by a whole number by using the following steps :
Step I     Check the whole number part of the dividend.
Step II     If the whole number part of the dividend is less than the divisor, then place a ‘0’  in the ones place in the quotient, other wise, go to step iii.
Step III  Divide the whole number part of the dividend.

Step IV Place the decimal point to the right of ones place in the quotient obtained in step I.

Step V  Divide the decimal part of the dividend by the divisor. If the digits of the dividend are exhausted, then place zeros to the right of dividend and remainder each time and continue the process.

Ex.1    Divide 93.45 by 15.
Sol.     We have,

Ex.2    Divide 42.8 by 0.02
Sol.     We have,

Ex.3    Divide 0.0024 by 0.04
Sol.    We have,

Ex4    The product of two decimals is 1.5008 . If one of them is 0.56, find the other. 
Sol.     Product of given decimals = 1.5008. 
        One decimal = 0.56.