5th Class Mathematics Operation of Decimals Multiplication of Decimals by Power of 10

   Multiplication of Decimals by Power of 10                

Step1: Shift the point in the decimal right as many places as there are zeroes the power of 10 contains.                                                           .                

Step 2 : If there are short of digits to the right of the point in the decimal, add zeroes right to it and follow the first step.

Multiply 23.256 by 100.

Explanation                

Power of ten (here 100) contains two zeroes, so point will shift two digit   right.                

Thus \[23.256\times 100\text{ }=2325.6.\]

Multiply 27.5 and 1000.                

Here power of 10 contains three zeroes, therefore, decimal point will shift three digit right but the decimal contains only one digit right to the point so add two zeroes right to it.                

Thus \[27.500\times 1000=27500\]  

Multiplication of a Decimal by a Whole Number                

Step 1: Remove the point from the decimal and multiply with the whole number simply.                

Step 2: Insert a point in the product so that the given decimal and the product have same number of decimal places.                

or                

Step 1: Convert the decimal into fraction.                

Step 2: Now multiply the fraction and the whole number.

Find the product of 45 and 78.63.                

Solution:                

Multiply 45 and 7863                

Thus \[45\times 7863\text{ }=353835\]                

Now place a point in 353835 so that 353835 and 78.63 have same decimal places.                

Thus the product \[45\times 78.63=3538.35\]                

Or

\[78.63=\frac{7863}{100}\]                

Thus \[45\times 78.63=45\times \frac{7863}{100}=\frac{7863\times 45}{100}=3538.35\]                

Multiplication of Decimals                

Step 1: Remove the point from the decimals and multiply them like whole numbers.                

Step 2: Insert a point in the product so that number of decimal places of the product is equal to the sum of the number of decimals places of the multiplier and the multiplicand.                

or                

Step 1: Convert the decimals into fractions.                

Step 2: Multiply numerator with numerator and denominator with denominator of the fractions.

Multiply 3.625 and 4.6.                

Solution:                

Multiply 3625 and 46                

Thus \[3625\times 46=166750\]                

Now 3.625 has three decimal places and 4.6 has one decimal place so place a point in 166750 so that it has four decimal places.                

Thus \[3.625\times 4.6=16.6750.\]                

Or                

\[3.625=\frac{3625}{1000}\]                       

\[4.6=\frac{46}{10}\]                

Thus \[3.625\times 4.6=\frac{3625}{1000}\times \frac{46}{10}=\frac{3625\times 46}{1000\times 10}=\frac{166750}{10000}=16.6750\]