# Multiplying decimals by 10, 100, and 1000

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=$5, point, 14, times, 10, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$5.14 \times 10=51.4$5, point, 14, times, 10, equals, 51, point, 4

## Let's try a few more.

$4.006 \times 10=$4, point, 006, times, 10, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$583.2 \times 10=$583, point, 2, times, 10, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$0.7761 \times 10=$0, point, 7761, times, 10, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

Multiplying by 10 moves every digit

*one place to the left*.$4.006 \times 10=40.06$4, point, 006, times, 10, equals, 40, point, 06

$583.2 \times 10=5832$583, point, 2, times, 10, equals, 5832

$0.7761 \times 10=7.761$0, point, 7761, times, 10, equals, 7, point, 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=$23, point, 8, times, 100, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$23.8 \times 100=2380$23, point, 8, times, 100, equals, 2380

## Let's try a few more.

$90.5 \times 100=$90, point, 5, times, 100, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$6.33 \times 100=$6, point, 33, times, 100, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$0.0047 \times 100=$0, point, 0047, times, 100, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

Multiplying by 100 moves every digit

*two places to the left*.$90.5 \times 100=9050$90, point, 5, times, 100, equals, 9050

$6.33 \times 100=633$6, point, 33, times, 100, equals, 633

$0.0047 \times 100=0.47$0, point, 0047, times, 100, equals, 0, point, 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=$0, point, 6, times, 1000, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$0.6 \times 1000=600$0, point, 6, times, 1000, equals, 600

## Let's try a few more.

$3.4 \times 1000=$3, point, 4, times, 1000, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$62.11 \times 1000=$62, point, 11, times, 1000, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$0.0577 \times 1000=$0, point, 0577, times, 1000, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

Multiplying by 1,000 moves every digit

*three places to the left*.$3.4 \times 1000=3400$3, point, 4, times, 1000, equals, 3400

$62.11 \times 1000=62{,}110$62, point, 11, times, 1000, equals, 62, comma, 110

$0.0577 \times 1000=57.7$0, point, 0577, times, 1000, equals, 57, point, 7

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

Multiplying by $1\blueD{0}$1, start color blueD, 0, end color blueD moves every digit

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

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

*$\purpleC{3}$start color purpleC, 3, end color purpleC places to the left*.Multiplying by $1\goldD{0{,}000}$1, start color goldD, 0, comma, 000, end color goldD moves every digit

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

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

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

*places to the left*.The number of zeros tells us how many times to move the digits.

Multiplying by $1\goldD{0{,}000}$1, start color goldD, 0, comma, 000, end color goldD moves every digit $\goldD4$start color goldD, 4, end color goldD

*places to the left*.Multiplying by $1\tealD{0{,}000{,}000}$1, start color tealD, 0, comma, 000, comma, 000, end color tealD moves every digit $\tealD7$start color tealD, 7, end color tealD

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

Use the pattern above to answer the following questions.

$71.55 \times 10{,}000=$71, point, 55, times, 10, comma, 000, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

$0.8 \times 1{,}000{,}000=$0, point, 8, times, 1, comma, 000, comma, 000, equals

**Your answer should be**- an integer, like $6$6
- a
*simplified proper*fraction, like $3/5$3, slash, 5 - a
*simplified improper*fraction, like $7/4$7, slash, 4 - a mixed number, like $1\ 3/4$1, space, 3, slash, 4
- an
*exact*decimal, like $0.75$0, point, 75 - a multiple of pi, like $12\ \text{pi}$12, space, p, i or $2/3\ \text{pi}$2, slash, 3, space, p, i

Multiplying by 10,000 moves every digit

*four places to the left*.$71.55 \times 10{,}000=715{,}500$71, point, 55, times, 10, comma, 000, equals, 715, comma, 500

Multiplying by 1,000,000 moves every digit

*six places to the left*.$0.8 \times 1{,}000{,}000=800{,}000$0, point, 8, times, 1, comma, 000, comma, 000, equals, 800, comma, 000

Multiplying and dividing decimals by 10, 100, and 1000