# 4th Class Mathematics Fractions and Decimals Multiplication of Decimals

Multiplication of Decimals

Category : 4th Class

### 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$~\text{42}\times \text{7562}=\text{3176}.0\text{4}$

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