In this post we will learn two methods to multiply decimals by whole number.

Both the methods will produce same result, so choose the one you find convenient.

**Multiplying decimal and whole number – Method 1**

To multiply the number, follow the below steps;

**(a) Convert the decimal into fraction**

Remove the decimal from number and insert 1 in denominator.

Now add 0’s in denominator as much as number of decimal place. **For example**;

If number has one decimal place, remove the decimal and insert denominator 10.

If number has 2 decimal place, remove the decimal and insert denominator 100**(b) Multiply numerator and denominator separately**

**(c)** **Convert the fraction back to decimals** by inserting decimal after places as much as number of zeros in denominator.

**For Example;**

If denominator contains 10, insert decimal point after 1 decimal place.

If denominator contains 100, place decimal point after 2 places.

Given below are solved questions for further understanding.

**Example 01**

Multiply 1.24 x 6**(a) Convert decimal into fraction.**

Number 1.24 contains 2 decimal places.

Converting the decimal into fraction;

1.24 ⟹ \mathtt{\frac{124}{100} \ }

**(b) Multiply the numbers **

\mathtt{\Longrightarrow \ \frac{124}{100} \ \times \frac{6}{1}}\\\ \\ \mathtt{\Longrightarrow \ \frac{124\ \times 6}{100}}\\\ \\ \mathtt{\Longrightarrow \ \frac{744}{100}}

**(c) Converting fraction back into decimal**

744/100 contains two zeros in denominator. So we will add decimal points after two places.

\mathtt{\frac{744}{100} \ \ \Longrightarrow \ 7.44}

Hence, 7.44 is the solution of multiplication.

**Example 02**

Multiply 4.5 x 12

**(a) Convert the decimal into fraction.**

4.5 contain one decimal place.

Converting 4.5 into fraction:

\mathtt{\ 4.5\ \Longrightarrow \ \frac{45}{10}}

**(b) Multiply the numerator and denominator separately.**

\mathtt{\Longrightarrow \ \frac{45}{10} \ \times \frac{12}{1}}\\\ \\ \mathtt{\Longrightarrow \ \frac{45\ \times 12}{10}}\\\ \\ \mathtt{\Longrightarrow \ \frac{540}{10}}

**(c) Convert the fraction back into decimal**

540/10 contain one zero in denominator. So will add decimal point after one place from right.

\mathtt{\frac{540}{10} \ \ \Longrightarrow \ 54.0}

Hence, 54 is the solution of given multiplication.

**Example 03**Multiply 3.123 x 6

**Solution****(a) Convert the decimals into fraction**

3.123 contains three decimals places.

Converting the decimal into fraction.

\mathtt{\ 3.123\ \Longrightarrow \ \frac{3.123}{1000}}

**(b) Multiply the numerator and denominator separately.**

\mathtt{\Longrightarrow \ \frac{3123}{1000} \ \times \frac{6}{1}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3123\ \times 6}{1000}}\\\ \\ \mathtt{\Longrightarrow \ \frac{18738}{1000}}

**(c) Converting fraction back to decimal**

18738/1000 contains three zero’s in denominator. So we put decimal point after three placed from the right.

\mathtt{\ \frac{18738}{1000} \ \ \Longrightarrow \ 18.738}

Hence, 18.738 is the solution of given multiplication.

**Multiply Decimal and Whole Number- Method 02**

To multiply the numbers follow the below steps;

**(a) Count the total decimal places in given number**

**(b) Remove the decimal point and multiply the numbers**

**(c) Insert the decimal back in final result**. The decimal place should be equal to total decimal point calculated before.

Given below are examples for your reference;

**Example 01**

Multiply 2.75 x 5

**(a) Finding number of decimal places**

2.75 ⟹ 2 decimal places

5 ⟹ 0 decimal place

Total decimal place = 2

**(b) Multiply the numbers without decimals**

275 x 5 = 1375

**(c) Insert decimal after 2 decimal places.**

⟹ 13.75

Hence, 13.7 is the solution.

**Example 02**

Multiply the decimal with whole number

2.5 x 36

**Solution****(a) Total Number of decimal place**

2.5 ⟹ 1 decimal place

36 ⟹ 0 decimal place

Total decimal place = 1

**(b) Multiply the numbers without decimals**

25 x 36 = 900**(c) Insert decimal after 1 decimal place**

⟹ 90.0

Hence, 90 is the solution for above multiplication.

**Example 03**

Multiply decimal with whole number

4.253 x 16

**Solution****(a) Total decimal places**

4.253 ⟹ 3 decimal places

16 ⟹ 0 decimal place

Total decimal places = 3

**(b) Multiply numbers without decimals**

4253 x 16 = 68048

**(c) Insert decimal after three places**

⟹ 68.048

Hence, 68.048 is the solution of multiplication.