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

# Multiplying decimals by 10, 100, and 1000

CCSS Math: 5.NBT.A.2

Practice multiplying decimals by 10, 100, and 1000.

# Part 1: Multiplying decimals by 10

Key idea: Multiplying by 10 moves every digit

*one place to the left*.Let's visualize it! Drag the dot all the way to the right.

$5.14 \times 10=$

**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 $2/3\ \text{pi}$

$5.14 \times 10=51.4$

## Let's try a few more.

$4.006 \times 10=$

**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 $2/3\ \text{pi}$

$583.2 \times 10=$

**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 $2/3\ \text{pi}$

$0.7761 \times 10=$

**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*.$4.006 \times 10=40.06$

$583.2 \times 10=5832$

$0.7761 \times 10=7.761$

# Part 2: Multiplying decimals by 100

Key idea: Multiplying by 100 moves every digit

*two places to the left*.Let's visualize it! Drag the dot all the way to the right.

*Notice that we add a zero to fill the empty place value.*$23.8 \times 100=$

**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 $2/3\ \text{pi}$

$23.8 \times 100=2380$

## Let's try a few more.

$90.5 \times 100=$

**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 $2/3\ \text{pi}$

$6.33 \times 100=$

**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 $2/3\ \text{pi}$

$0.0047 \times 100=$

**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*.$90.5 \times 100=9050$

$6.33 \times 100=633$

$0.0047 \times 100=0.47$

# Part 3: Multiplying decimals by 1,000

Key idea: Multiplying by 1,000 moves every digit

*three places to the left*.Let's visualize it! Drag the dot all the way to the right.

*Notice that we add zeros to fill the empty place values.*$0.6 \times 1000=$

**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 $2/3\ \text{pi}$

$0.6 \times 1000=600$

## Let's try a few more.

$3.4 \times 1000=$

**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 $2/3\ \text{pi}$

$62.11 \times 1000=$

**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 $2/3\ \text{pi}$

$0.0577 \times 1000=$

**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 1,000 moves every digit

*three places to the left*.$3.4 \times 1000=3400$

$62.11 \times 1000=62{,}110$

$0.0577 \times 1000=57.7$

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

Multiplying by $1\blueD{0}$ moves every digit

*$\blueD{1}$ place to the left*.Multiplying by $1\greenD{00}$ moves every digit

*$\greenD{2}$ places to the left*.Multiplying by $1{,}\purpleC{000}$ moves every digit

*$\purpleC{3}$ places to the left*.Multiplying by $1\goldD{0{,}000}$ 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 left*.Multiplying by $1\tealD{0{,}000{,}000}$ 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 left*.The number of zeros tells us how many times to move the digits.

Multiplying by $1\goldD{0{,}000}$ moves every digit $\goldD4$

*places to the left*.Multiplying by $1\tealD{0{,}000{,}000}$ moves every digit $\tealD7$

*places to the left*.# Part 5: Challenge time!

Use the pattern above to answer the following questions.

$71.55 \times 10{,}000=$

**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 $2/3\ \text{pi}$

$0.8 \times 1{,}000{,}000=$

**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 $2/3\ \text{pi}$

Multiplying by 10,000 moves every digit

*four places to the left*.$71.55 \times 10{,}000=715{,}500$

Multiplying by 1,000,000 moves every digit

*six places to the left*.$0.8 \times 1{,}000{,}000=800{,}000$