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{10} moves every digit one place to the right.

Let's visualize it! Drag the dot all the way to the right.
5.14÷10=5.14 \div 10=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

5.14÷10=0.5145.14 \div 10=0.514

Let's try a few more dividing by 1010:

44.2÷10=44.2 \div 10=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

145.18÷10=145.18 \div 10=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

0.678÷10=0.678 \div 10=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Dividing by 10{10} moves every digit one place to the right.
44.2÷10=4.4244.2 \div 10=4.42
145.18÷10=14.518145.18 \div 10=14.518
0.678÷10=0.06780.678 \div 10=0.0678

And one multiplying by 1010 (for review):

0.933×10=0.933 \times 10=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Multiplying by 10{10} moves every digit one place to the left.
0.933×10=9.330.933 \times 10=9.33

Part 2: Dividing decimals by 100

Key idea: Dividing by 100{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÷100=2.8 \div 100=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

2.8÷100=0.0282.8 \div 100=0.028

Let's try a few more dividing by 100100:

6.33÷100=6.33 \div 100=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

71.005÷100=71.005 \div 100=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

189.2÷100=189.2 \div 100=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Dividing by 100{100} moves every digit two places to the right.
6.33÷100=0.06336.33 \div 100=0.0633
71.005÷100=0.7100571.005 \div 100=0.71005
189.2÷100=1.892189.2 \div 100=1.892

And one multiplying by 100100 (for review):

5.4×100=5.4 \times 100=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Multiplying by 100{100} moves every digit two places to the left.
5.4×100=5405.4 \times 100=540

Part 3: Dividing decimals by 1000

Key idea: Dividing by 1000{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÷1000=0.6 \div 1000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

0.6÷1000=0.00060.6 \div 1000=0.0006

Let's try a few more dividing by 10001000:

7500.9÷1000=7500.9 \div 1000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

0.1÷1000=0.1 \div 1000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

623.88÷1000=623.88 \div 1000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Dividing by 1000{1000} moves every digit three places to the right.
7500.9÷1000=7.50097500.9 \div 1000=7.5009
0.1÷1000=0.00010.1 \div 1000=0.0001
623.88÷1000=0.62388623.88 \div 1000=0.62388

And one multiplying by 10001000 (for review):

0.0043×1000=0.0043 \times 1000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Multiplying by 1000{1000} moves every digit three places to the left.
0.0043×1000=4.30.0043 \times 1000=4.3

Part 4: Let's look at the pattern.

Dividing by 101\blueD{0} moves every digit 1\blueD{1} place to the right.
Dividing by 1001\greenD{00} moves every digit 2\greenD{2} places to the right.
Dividing by 10001\purpleC{000} moves every digit 3\purpleC{3} places to the right.
Dividing by 100,0001\tealD{00{,}000} moves every digit
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
places to the right.
Dividing by 1,000,0001\goldD{{,}000{,}000} moves every digit
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
places to the right.

The number of zeros tells us how many times to move the digits.
Dividing by 1,000,0001\goldD{{,}000{,}000} moves every digit 6\goldD6 places to the right.
Dividing by 100,0001\tealD{00{,}000} moves every digit 5\tealD5 places to the right.

Part 5: Challenge time!

Use the pattern above to answer the following questions.
333.4÷100,000=333.4 \div 100{,}000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

29.7÷1,000,000=29.7 \div 1{,}000{,}000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Dividing by 100,000{100{,}000} moves every digit five places to the right.
333.4÷100,000=0.003334333.4 \div 100{,}000=0.003334
Dividing by 1,000,000{1{,}000{,}000} moves every digit six places to the right.
29.7÷1,000,000=0.000029729.7 \div 1{,}000{,}000=0.0000297

And a multiplication challenge:

0.055×10,000=0.055 \times 10{,}000=
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Multiplying by 10,000{10{,}000} moves every digit four places to the left.
0.055×10,000=5500.055 \times 10{,}000=550