Introduction

To multiply a decimal by a one-digit whole number, such as 5.2 \times 7, we follow the two steps below.

Step 1. First, ignore the decimal point and multiply as if both numbers were whole numbers:

\begin{align*} & \begin{array}{ccccc} & & \!\!\!\!\! \substack{ \\ \color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 5 \!\!\!\! & \!\!\!\!\!\!\! . 2 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & \!\!\!\! {7} \!\!\!\! \\ \hline & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 6 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \end{array} \end{align*}

Step 2. Then, insert the decimal point in the result to have the same number of decimal places as the decimal factor.

Here, there is \color{blue}1 decimal place in 5.2, so the product will also have {\color{blue}{1}} decimal place. We take our value of 364 and insert a decimal point to make a number with \color{blue}1 decimal place:

36\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{4}_{\large\text{[math]\color{blue}1[/math] digit}}

Therefore, 5.2 \times 7 = 36.4 \, .

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Example: Multiplying a Decimal With One Decimal Place

What is 28.6 multiplied by 7?

EXPLANATION

First, we ignore the decimal point and multiply as if both numbers were whole numbers:

\begin{align*} & \begin{array}{ccccc} & & \!\!\!\!\! \substack{ \\ \color{blue}6}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}4}{} \!\!\!\! & \\ & & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\!\!\!\! . 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! 7 \!\!\!\! \\ \hline & \!\!\!\! 2 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \end{array} \end{align*}

Then, we insert the decimal point in the result to have the same number of decimal places as the decimal factor.

There is \color{blue}1 decimal place in 28.6, so the product will also have {\color{blue}{1}} decimal place. We take our value of 2002 and insert a decimal point to make a number with \color{blue}1 decimal place:

200\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{2}_{\large\text{[math]\color{blue}1[/math] digit}}

Therefore, 28.6 \times 7 = 200.2 \, .

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Practice: Multiplying a Decimal With One Decimal Place

$3.6 \times 2 =$

a
b
c
d
e
Practice: Multiplying a Decimal With One Decimal Place

$4.1 \times 3 =$

a
 $0.123$
b
 $1.2$
c
 $12.3$
d
 $12$
e
 $1.23$
Practice: Multiplying a Decimal With One Decimal Place

$14.2 \times 9 =$

a
 $127.8$
b
 $12.68$
c
 $97.8$
d
 $12.78$
e
 $9.78$
Practice: Multiplying a Decimal With One Decimal Place

$181.5 \times 2 =$

a
 $26.20$
b
 $363$
c
 $263$
d
 $26.3$
e
 $36.30$
Multiplying Decimals With More Than One Decimal

The same idea works for multiplying a whole number by a decimal with any number of decimal places.

For example, let's find the value of 8.29 \times 4.

First, we ignore the decimal point and multiply as if both numbers were whole numbers:

\begin{align*} & \begin{array}{ccccc} & & \!\!\!\!\! \substack{ \\ \color{blue}1}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 8 \!\!\!\! & \!\!\!\!\!\!\! . 2 \!\!\!\! & \!\!\!\! 9 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} \end{align*}

Then, we insert the decimal point in the result to have the same number of decimal places as the decimal factor.

There are \color{blue}2 decimal places in 8.29, so the product will also have {\color{blue}{2}} decimal places. We take our value of 3316 and insert a decimal point to make a number with \color{blue}2 decimal places:

33\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{16}_{\large\text{[math]\color{blue}2[/math] digits}}

Therefore, 8.29 \times 4 = 33.16 \,.

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Example: Multiplying Decimal With Two Decimal Places

What is 13.96 multiplied by 6?

EXPLANATION

First, we ignore the decimal point and multiply as if both numbers were whole numbers:

\begin{align*} & \begin{array}{ccccc} & & \!\!\!\!\! \substack{ \\ \color{blue}2}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}5}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\!\!\!\! . 9 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! 6 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 3 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} \end{align*}

Then, we insert the decimal point in the result to have the same number of decimal places as the decimal factor.

There are \color{blue}2 decimal places in 13.96, so the product will also have {\color{blue}{2}} decimal places. We take our value of 8376 and insert a decimal point to make a number with \color{blue}2 decimal places:

83\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{76}_{\large\text{[math]\color{blue}2[/math] digits}}

Therefore, 13.96 \times 6 = 83.76 \,.

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Practice: Multiplying Decimal With Two Decimal Places

$3.14 \times 5 =$

a
 $157$
b
 $1.54$
c
 $15.7$
d
 $154$
e
 $15.4$
Practice: Multiplying Decimal With Two Decimal Places

$23.94 \times 6 =$

a
 $142.94$
b
 $144.04$
c
 $143.64$
d
 $1.4364$
e
 $14.364$
Example: Multiplying Decimal With Three Decimal Places

0.614 \times 3 =

EXPLANATION

First, we ignore the decimal point and multiply as if both numbers were whole numbers:

\begin{align*} & \begin{array}{ccccc} & & \!\!\!\!\! \substack{ \\ \color{blue}1}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}\phantom{0}}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}1}{} \!\!\!\! & \\ & & \!\!\!\! 0 \!\!\!\! & \!\!\!\!\!\!\! . 6 \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 4 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! 3 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 8 \!\!\!\! & \!\!\!\! 4 \!\!\!\! & \!\!\!\! 2 \!\!\!\! \end{array} \end{align*}

Then, we insert the decimal point in the result to have the same number of decimal places as the decimal factor.

There are \color{blue}3 decimal places in 0.614, so the product will also have {\color{blue}{3}} decimal places. We take our value of 1842 and place a decimal point to make a number with \color{blue}3 decimal places:

1\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{842}_{\large\text{[math]\color{blue}3[/math] digits}}

Therefore, 0.614 \times 3 = 1.842.

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Practice: Multiplying Decimal With Three Decimal Places

$0.206 \times 7 = $

a
 $0.242$
b
 $144.2$
c
 $14.42$
d
 $1.442$
e
 $0.442$
Practice: Multiplying Decimal With Three Decimal Places

$1.369 \times 6 = $

a
 $821.4$
b
 $8.724$
c
 $82.14$
d
 $8.214$
e
 $8.414$
Example: Word Problems

Bart bought 4 tickets to go with his friends to the movie theater. If he paid \[math]12.69 for each ticket, how much did Bart spend in total to buy the tickets?

EXPLANATION

To find out how much Bart spent to buy the tickets, we need to multiply \[math]12.69 by 4.

First, we ignore the decimal point and multiply as if both numbers were whole numbers:

\begin{align*} & \begin{array}{ccccc} & & \!\!\!\!\! \substack{ \\ \color{blue}1}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}2}{} \!\!\!\! & \!\!\!\!\! \substack{ \\ \color{blue}3}{} \!\!\!\! & \\ & & \!\!\!\! 1 \!\!\!\! & \!\!\!\! 2 \!\!\!\! & \!\!\!\!\!\!\! . 6 \!\!\!\! & \!\!\!\! 9 \!\!\!\! \\ \!\!\!\!\times\!\!\!\! & & & & & \!\!\!\! 4 \!\!\!\! \\ \hline & \!\!\!\! \!\!\!\! & \!\!\!\! 5 \!\!\!\! & \!\!\!\! 0 \!\!\!\! & \!\!\!\! 7 \!\!\!\! & \!\!\!\! 6 \!\!\!\! \end{array} \end{align*}

Then, we insert the decimal point in the result to have the same number of decimal places as the decimal factor.

There are \color{blue}2 decimal places in 12.69, so the product will also have {\color{blue}{2}} decimal places. We take our value of 5076 and insert a decimal point to make a number with \color{blue}2 decimal places:

50\,\overset{\color{red}\downarrow}{\color{red}\bbox[2px, lightgray]{.}}\!\!\!\underbrace{76}_{\large\text{[/math]\color{blue}2[math] digits}}

So, 12.69 \times 4 = 50.76 \,.

Therefore, Bart spent \[/math]50.76 to buy the tickets.

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Practice: Word Problems

Jim bought five sacks of potatoes for his restaurant. If each sack weighs $6.4 $ kilograms, how many kilograms of potatoes did Jim buy in total?

a
 $32.2$ kilograms
b
 $3.2$ kilograms
c
 $320$ kilograms
d
 $30$ kilograms
e
 $32$ kilograms
Practice: Word Problems

A rope is cut into $8$ equal parts, each of which is $24.8$ meters long. How long was the rope originally?

a
 $198.4$ meters
b
 $189.04$ meters
c
 $19.84$ meters
d
 $18.94$ meters
e
 $189.4$ meters
Why Does Our Method Work?

Throughout this lesson, we've practiced multiplying a decimal by a whole number using the following technique:

  • First, we multiply the numbers without the decimal parts.

  • Then, we count the decimal places in the decimal factor and create a number from our answer with this many decimal places.

To see why this works, consider the following example:

6 \times 3.2

Expressing 3.2 as a decimal fraction, we can write this product as follows:

6 \times \dfrac{32}{10}

Since every fraction is equivalent to a division, we can write this as

6 \times32 \div 10.

Let's add parentheses to make this easier to read:

\left(6 \times32\right) \div 10

Therefore, to calculate 6\times 3.2, we follow two steps:

  • First, we calculate the value of 6\times 32.

  • Then, we divide the final answer by 10. To do this, we take the answer from the first step and move the decimal point by one space to the left.

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