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, point, 14, times, 10, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

5, point, 14, times, 10, equals, 51, point, 4

Let's try a few more.

4, point, 006, times, 10, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

583, point, 2, times, 10, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

0, point, 7761, times, 10, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Multiplying by 10 moves every digit one place to the left.
4, point, 006, times, 10, equals, 40, point, 06
583, point, 2, times, 10, equals, 5832
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, point, 8, times, 100, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

23, point, 8, times, 100, equals, 2380

Let's try a few more.

90, point, 5, times, 100, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

6, point, 33, times, 100, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

0, point, 0047, times, 100, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Multiplying by 100 moves every digit two places to the left.
90, point, 5, times, 100, equals, 9050
6, point, 33, times, 100, equals, 633
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, point, 6, times, 1000, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

0, point, 6, times, 1000, equals, 600

Let's try a few more.

3, point, 4, times, 1000, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

62, point, 11, times, 1000, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

0, point, 0577, times, 1000, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Multiplying by 1,000 moves every digit three places to the left.
3, point, 4, times, 1000, equals, 3400
62, point, 11, times, 1000, equals, 62, comma, 110
0, point, 0577, times, 1000, equals, 57, point, 7

Part 4: Let's look at the pattern.

Multiplying by 1, start color blueD, 0, end color blueD moves every digit start color blueD, 1, end color blueD place to the left.
Multiplying by 1, start color greenD, 00, end color greenD moves every digit start color greenD, 2, end color greenD places to the left.
Multiplying by 1, comma, start color purpleC, 000, end color purpleC moves every digit start color purpleC, 3, end color purpleC places to the left.
Multiplying by 1, start color goldD, 0, comma, 000, end color goldD moves every digit
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
places to the left.
Multiplying by 1, start color tealD, 0, comma, 000, comma, 000, end color tealD moves every digit
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 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, start color goldD, 0, comma, 000, end color goldD moves every digit start color goldD, 4, end color goldD places to the left.
Multiplying by 1, start color tealD, 0, comma, 000, comma, 000, end color tealD moves every digit 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, point, 55, times, 10, comma, 000, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

0, point, 8, times, 1, comma, 000, comma, 000, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

Multiplying by 10,000 moves every digit four places to the left.
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, point, 8, times, 1, comma, 000, comma, 000, equals, 800, comma, 000