## Multiplying and dividing decimals by 10, 100, and 1000

# 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.

$5.14 \div 10=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$5.14 \div 10=0.514$

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

$44.2 \div 10=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$145.18 \div 10=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$0.678 \div 10=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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):

$0.933 \times 10=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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.*$2.8 \div 100=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$2.8 \div 100=0.028$

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

$6.33 \div 100=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$71.005 \div 100=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$189.2 \div 100=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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):

$5.4 \times 100=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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.*$0.6 \div 1000=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$0.6 \div 1000=0.0006$

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

$7500.9 \div 1000=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$0.1 \div 1000=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

$623.88 \div 1000=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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):

$0.0043 \times 1000=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

**places to the right**.Dividing by $1\goldD{{,}000{,}000}$ moves every digit

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

**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.

$333.4 \div 100{,}000=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

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:

$0.055 \times 10{,}000=$

**Your answer should be**- an integer, like $6$
- a
*simplified proper*fraction, like $3/5$ - a
*simplified improper*fraction, like $7/4$ - a mixed number, like $1\ 3/4$
- an
*exact*decimal, like $0.75$ - a multiple of pi, like $12\ \text{pi}$ or $2/3\ \text{pi}$

Multiplying by ${10{,}000}$ moves every digit

**four places to the left**.$0.055 \times 10{,}000=550$