Multiplication of Decimals
Category : 4th Class
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\[~\text{42}\times \text{7562}=\text{3176}.0\text{4}\]
You need to login to perform this action.
You will be redirected in
3 sec