4th Class Mathematics Decimals and Fractions Multiplication of Decimals

Multiplication of Decimals  

  Multiplication of Decimals by Power of 10  

Case 1: When a decimal is multiplied by 10. Like\[\text{8}.\text{6542}\times \text{1}0\] The decimal is shifted one digit right. Thus\[\text{8}.\text{6542}\times \text{1}0=\text{86}.\text{542}\]  

Case 2: When a decimal is multiplied by 100. Like\[\text{8}.\text{6542}\times \text{1}00\] The decimal is shifted two digit right. Thus\[\text{8}.\text{6542}\times \text{1}00=\text{865}.\text{42}\]

Case 3: When a decimal is multiplied by 1000. Like\[~\text{8}.\text{6542}\times \text{1}000\] The decimal is shifted three digit right. Thus \[\text{8}.\text{6542}\times \text{1}000=\text{8654}.\text{2}\]  

Note:    As you increase the power of 10 by one, the decimal point shift one digit right.  

For example: \[\text{2}.\text{35682}\times \text{1}{{\text{0}}^{2}}=\text{235}.\text{682}\] \[2.35682\times {{10}^{3}}=2356.82\] \[2.35682\times {{10}^{4}}=23568.2\]  

\[\mathbf{Multiply:394}\mathbf{.5607\times 1000}\]

Solution:

\[~\text{394}.\text{56}0\text{7}\times \text{1}000=\text{39456}0.\text{7}\]  

\[\mathbf{Multiply:100}\mathbf{.15\times 100}\]

Solution:

\[\text{1}00.\text{15}\times \text{1}00=\text{1}00\text{15}\]  

\[\mathbf{Multiply:494}\mathbf{.3607\times 1000}\]

(a) 234343.787                                  

(b) 446676.9786

(c) 23424.56757                                

(d) 494360.7

(e) None of these

Answer (d)

Explanation-\[\text{494}.\text{36}0\text{7}\times \text{1}000=\text{49436}0.\text{7}\]  

Multiplication of a Decimal and a Whole Number

Step 1: Remove the point from the decimal and multiply the numbers like multiplication of whole numbers.

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

Find the product of 42 and 75.62.

Solution:

Multiply 42 and 7562 Thus \[\text{42}\times \text{7562}=\text{3176}0\text{4}\] Now place a point in 317604 such that 317604 and 75.62 have same decimal places. Thus the product of\[~\text{42}\times \text{7562}=\text{3176}.0\text{4}\]