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.
5.14×10=5.14 \times 10=
5.14×10=51.45.14 \times 10=51.4

Let's try a few more.

4.006×10=4.006 \times 10=
583.2×10=583.2 \times 10=
0.7761×10=0.7761 \times 10=
Multiplying by 10 moves every digit one place to the left.
4.006×10=40.064.006 \times 10=40.06
583.2×10=5832583.2 \times 10=5832
0.7761×10=7.7610.7761 \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.
23.8×100=23.8 \times 100=
23.8×100=238023.8 \times 100=2380

Let's try a few more.

90.5×100=90.5 \times 100=
6.33×100=6.33 \times 100=
0.0047×100=0.0047 \times 100=
Multiplying by 100 moves every digit two places to the left.
90.5×100=905090.5 \times 100=9050
6.33×100=6336.33 \times 100=633
0.0047×100=0.470.0047 \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.
0.6×1000=0.6 \times 1000=
0.6×1000=6000.6 \times 1000=600

Let's try a few more.

3.4×1000=3.4 \times 1000=
62.11×1000=62.11 \times 1000=
0.0577×1000=0.0577 \times 1000=
Multiplying by 1,000 moves every digit three places to the left.
3.4×1000=34003.4 \times 1000=3400
62.11×1000=62,11062.11 \times 1000=62{,}110
0.0577×1000=57.70.0577 \times 1000=57.7

Part 4: Let's look at the pattern.

Multiplying by 101\blueD{0} moves every digit 1\blueD{1} place to the left.
Multiplying by 1001\greenD{00} moves every digit 2\greenD{2} places to the left.
Multiplying by 1,0001{,}\purpleC{000} moves every digit 3\purpleC{3} places to the left.
Multiplying by 10,0001\goldD{0{,}000} moves every digit
places to the left.
Multiplying by 10,000,0001\tealD{0{,}000{,}000} moves every digit
places to the left.
The number of zeros tells us how many times to move the digits.
Multiplying by 10,0001\goldD{0{,}000} moves every digit 4\goldD4 places to the left.
Multiplying by 10,000,0001\tealD{0{,}000{,}000} moves every digit 7\tealD7 places to the left.

Part 5: Challenge time!

Use the pattern above to answer the following questions.
71.55×10,000=71.55 \times 10{,}000=
0.8×1,000,000=0.8 \times 1{,}000{,}000=
Multiplying by 10,000 moves every digit four places to the left.
71.55×10,000=715,50071.55 \times 10{,}000=715{,}500
Multiplying by 1,000,000 moves every digit six places to the left.
0.8×1,000,000=800,0000.8 \times 1{,}000{,}000=800{,}000