# Dividing decimals by 10, 100, and 1000

CCSS Math: 5.NBT.A.2
Practice dividing decimals by 10, 100, and 1000.

# Part 1: Dividing decimals by 10

### Key idea: Dividing by ${10}$ moves every digit one place to the right.

Let's visualize it! Drag the dot all the way to the right.
$5.14 \div 10=$

$5.14 \div 10=0.514$

## Let's try a few more dividing by $10$:

$44.2 \div 10=$

$145.18 \div 10=$

$0.678 \div 10=$

Dividing by ${10}$ moves every digit one place to the right.
$44.2 \div 10=4.42$
$145.18 \div 10=14.518$
$0.678 \div 10=0.0678$

### And one multiplying by $10$ (for review):

$0.933 \times 10=$

Multiplying by ${10}$ moves every digit one place to the left.
$0.933 \times 10=9.33$

# Part 2: Dividing decimals by 100

### Key idea: Dividing by ${100}$ moves every digit two places to the right.

Let's visualize it! Drag the dot all the way to the right.
Notice that we add zeros to fill the empty place values.
$2.8 \div 100=$

$2.8 \div 100=0.028$

## Let's try a few more dividing by $100$:

$6.33 \div 100=$

$71.005 \div 100=$

$189.2 \div 100=$

Dividing by ${100}$ moves every digit two places to the right.
$6.33 \div 100=0.0633$
$71.005 \div 100=0.71005$
$189.2 \div 100=1.892$

### And one multiplying by $100$ (for review):

$5.4 \times 100=$

Multiplying by ${100}$ moves every digit two places to the left.
$5.4 \times 100=540$

# Part 3: Dividing decimals by 1000

### Key idea: Dividing by ${1000}$ moves every digit three places to the right.

Let's visualize it! Drag the dot all the way to the right.
Notice that we add zeros to fill the empty place values.
$0.6 \div 1000=$

$0.6 \div 1000=0.0006$

## Let's try a few more dividing by $1000$:

$7500.9 \div 1000=$

$0.1 \div 1000=$

$623.88 \div 1000=$

Dividing by ${1000}$ moves every digit three places to the right.
$7500.9 \div 1000=7.5009$
$0.1 \div 1000=0.0001$
$623.88 \div 1000=0.62388$

### And one multiplying by $1000$ (for review):

$0.0043 \times 1000=$

Multiplying by ${1000}$ moves every digit three places to the left.
$0.0043 \times 1000=4.3$

# Part 4: Let's look at the pattern.

Dividing by $1\blueD{0}$ moves every digit $\blueD{1}$ place to the right.
Dividing by $1\greenD{00}$ moves every digit $\greenD{2}$ places to the right.
Dividing by $1\purpleC{000}$ moves every digit $\purpleC{3}$ places to the right.
Dividing by $1\tealD{00{,}000}$ moves every digit
places to the right.
Dividing by $1\goldD{{,}000{,}000}$ moves every digit
places to the right.

The number of zeros tells us how many times to move the digits.
Dividing by $1\goldD{{,}000{,}000}$ moves every digit $\goldD6$ places to the right.
Dividing by $1\tealD{00{,}000}$ moves every digit $\tealD5$ places to the right.

# Part 5: Challenge time!

Use the pattern above to answer the following questions.
$333.4 \div 100{,}000=$

$29.7 \div 1{,}000{,}000=$

Dividing by ${100{,}000}$ moves every digit five places to the right.
$333.4 \div 100{,}000=0.003334$
Dividing by ${1{,}000{,}000}$ moves every digit six places to the right.
$29.7 \div 1{,}000{,}000=0.0000297$

### And a multiplication challenge:

$0.055 \times 10{,}000=$

Multiplying by ${10{,}000}$ moves every digit four places to the left.
$0.055 \times 10{,}000=550$