# Multiplying decimals by whole numbers

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.