Introduction

We can use place value charts to divide decimals by 10. For instance, to find the value of

28 \div 10,

we perform the following steps.

Step 1. Write down the place value chart for 28 :

tens ones tenths
2 8 .

Step 2. Move all digits by one place to the right.

tens ones tenths
2 . 8

Therefore, 28\div 10 = 2.8 \, .

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Example: Finding Missing Values in a Place Value Chart When Dividing By Ten

Beth calculates 12.5 \div 10 and places her answer in the table below. From left to right, what are the missing digits?

ones tenths hundredths
\fbox{[math]\phantom{0}[/math]} . 2 \fbox{[math]\phantom{0}[/math]}
EXPLANATION

First, we write down the place value chart for 12.5\mathbin{:}

tens ones tenths hundredths
1 2 . 5

Then, we move all digits by one place to the right.

tens ones tenths hundredths
\bbox[3pt, lightgray]{1} . 2 \bbox[3pt, lightgray]{5}

Hence, 12.5\div 10 = 1.25\, . The missing digits are therefore 1 and 5.

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Practice: Finding Missing Values in a Place Value Chart When Dividing By Ten

Dan calculates $6.14\div 10$ and places his answer in the table below. From left to right, what are the missing digits?

ones tenths hundredths thousandths
. $\fbox{$\phantom{0}$}$ $1$ $\fbox{$\phantom{0}$}$
a
 $0$ and $4$
b
 $6$ and $0$
c
 $1$ and $4$
d
 $0$ and $0$
e
 $6$ and $4$
Practice: Finding Missing Values in a Place Value Chart When Dividing By Ten

William calculates $19.3 \div 10$ and places his answer in the table below. From left to right, what are the missing digits?

ones tenths hundredths
$\fbox{$\phantom{0}$}$ . $9$ $\fbox{$\phantom{0}$}$
a
 $1$ and $0$
b
 $0$ and $3$
c
 $9$ and $3$
d
 $4$ and $9$
e
 $1$ and $3$
Example: Dividing by Ten Using a Place Value Chart

Find the place value chart of 225 \div 10.

EXPLANATION

First, we write down the place value chart for 225\mathbin{:}

hundreds tens ones tenths
2 2 5 .

Then, we move all digits by one place to the right.


hundreds tens ones tenths
2 2 . 5
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Practice: Dividing by Ten Using a Place Value Chart

Find the place value chart of $53.2\div 10.$

a
tens ones tenths hundredths thousandths
$5$ . $3$ $2$
b
tens ones tenths hundredths thousandths
$0$ . $5$ $3$ $2$
c
tens ones tenths hundredths thousandths
$5$ $3$ . $2$
d
tens ones tenths hundredths thousandths
$5$ . $3$ $2$
e
tens ones tenths hundredths thousandths
$5$ . $3$ $2$
Practice: Dividing by Ten Using a Place Value Chart

Find the place value chart of $2.8\div 10.$

a
tens ones tenths hundredths
$2$ $0$ . $0$ $8$
b
tens ones tenths hundredths
$2$ $8$ . $0$ $0$
c
tens ones tenths hundredths
$0$ . $2$ $8$
d
tens ones tenths hundredths
$2$ $0$ . $8$ $0$
e
tens ones tenths hundredths
$2$ . $0$ $8$
Dividing Decimals by Larger Powers of Ten

When dividing by a power of ten, we shift the digits in the place value chart to the right by the number of zeros in the power of ten.

To illustrate, let's find the value of 47.2 \div 100.

Step 1. Write down the place value chart for 47.2\mathbin{:}

tens ones tenths hundredths thousandths
4 7 . 2

Step 2. Determine the number of places to move. We're dividing by 100, which has \color{blue}2 zeros, so we move all values to the right by \color{blue}2 places:

tens ones tenths hundredths thousandths
. 4 7 2

Step 3. Put zero in all empty cells that are to the right of the decimal point. We can also put a zero in the ones place if it is empty.

tens ones tenths hundredths thousandths
0 . 4 7 2

Therefore, 47.2\div 100 = 0.472 \, .

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Example: Dividing by One Hundred Using a Place Value Chart

What is the missing digit in the place value chart below for 0.3\div 100 ?

ones tenths hundredths thousandths
0 . 0 \fbox{[math]\phantom{0}[/math]} 3
EXPLANATION

First, we write down the place value chart for 0.3\mathbin{:}

ones tenths hundredths thousandths
0 . 3

Then, we determine the number of places to move. We're dividing by 100 , which has 2 zeros, so we move all values to the right by 2 places:

ones tenths hundredths thousandths
. 0 3

Finally, we put zeros in all empty cells that are to the right of the decimal point, and also in the empty ones place:

ones tenths hundredths thousandths
0 . 0 \bbox[3pt, lightgray]{0} 3

Therefore, 0.3\div 100 = 0.003 \, . The missing digit is 0.

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Practice: Dividing by One Hundred Using a Place Value Chart

What are the missing digits in the place value chart below for $0.6\div 100?$

ones tenths hundredths thousandths
$0$ . $0$ $\fbox{$\phantom{0}$}$ $\fbox{$\phantom{0}$}$
a
 $3$ and $0$
b
 $6$ and $0$
c
 $0$ and $6$
d
 $0$ and $3$
e
 $1$ and $2$
Practice: Dividing by One Hundred Using a Place Value Chart

From left to right, what are the missing digits in the place value chart below for $2.1\div 100 ?$

tens ones tenths hundredths thousandths
$0$ . $\fbox{$\phantom{0}$}$ $\fbox{$\phantom{0}$}$ $1$
a
 $1$ and $2$
b
 $0$ and $1$
c
 $0$ and $0$
d
 $0$ and $2$
e
 $2$ and $0$
Example: Dividing by One Thousand Using a Place Value Chart

From left to right, what are the missing digits in the place value chart below for 246\div 1,000?

ones tenths hundredths thousandths
\fbox{[math]\phantom{0}[/math]} . 2 \fbox{[math]\phantom{0}[/math]} 6
EXPLANATION

First, we write down the place value chart for 246\mathbin{:}

hundreds tens ones tenths hundredths thousandths
2 4 6 .

Then, we determine the number of places to move. We're dividing by 1,000, which has 3 zeros, so we move all values to the right by 3 places:

hundreds tens ones tenths hundredths thousandths
. 2 4 6

Finally, we put zeros in all empty cells that are to the right of the decimal point, and also in the empty ones place:

hundreds tens ones tenths hundredths thousandths
\bbox[3pt, lightgray]{0} . 2 \bbox[3pt, lightgray]{4} 6

Therefore, 246\div 1,000= 0.246 \, . The missing digits are 0 and 4.

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Practice: Dividing by One Thousand Using a Place Value Chart

From left to right, what are the missing digits in the place value chart below for $39\div 1,000?$

tens ones tenths hundredths thousandths
$\fbox{$\phantom{0}$}$ . $0$ $3$ $\fbox{$\phantom{0}$}$
a
 $0$ and $1$
b
 $9$ and $0$
c
 $0$ and $0$
d
 $1$ and $0$
e
 $0$ and $9$
Practice: Dividing by One Thousand Using a Place Value Chart

From left to right, what are the missing digits in the place value chart below for $625\div 1,000 ?$

ones tenths hundredths thousandths
$0$ . $\fbox{$\phantom{0}$}$ $2$ $\fbox{$\phantom{0}$}$
a
 $0$ and $6$
b
 $6$ and $5$
c
 $3$ and $7$
d
 $2$ and $5$
e
 $6$ and $0$
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