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Multiplication and Division by Powers of 10
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A power of 10 is a number that can be written as 10 raised to a power or exponent. \( 10 ^1 = 10, 10^2 = 100, 10^3 = 1000, {\text{and}}\:\ 10^4 = 10000 \) are all examples of powers of 10. Multiplying or dividing by these powers simply requires us to move the decimal place of the number that we’re multiplying or dividing. The following video will explain this and show some examples.

Multiplication and division by powers of 10

Video Source (07:45 mins) | Transcript

Multiplication by a power of 10: move the decimal to the RIGHT the same number of times as the number of 0’s in the power of 10.

Example: \(54.2 × 100 = 5420\) or 5420.0 The decimal moved two spaces to the right.

Division by a power of 10: move the decimal to the left the same number of times as the number of 0’s in the power of 10.

Example: \(5420.0 ÷ 100 = 54.2\) The decimal moved two spaces to the left.

Additional Resources

Practice Problems

Evaluate the following expression:
  1. \(86 × 10 = ?\) (
    Solution
    x
    Solution: 860
    Details:
    In this image we see the numbers 86 and 860 written inside a table. The columns of the table are labeled with the number place values.The number 86 is in the first row of the table. The 8 is in the tens column and the 6 is just to the right in the ones column. In the next row down is the number 860. The 8 is in the hundreds column while the 6 is in the tens column and the 0 is in the ones column.
    In this example, we can see how our original number, 86 when multiplied by 10 moves from 8 tens and 6 ones to 8 hundreds, 6 tens and 0 ones. When multiplying by 10, each number moved one space to the left in the place value chart.
    )
  2. \(295 ÷ 10 = ?\) (
    Solution
    x
    Solution: \(29.5\)
    Details:
    In this image we see the numbers 295 and 29 point 5 written inside a table. The columns of the table are labeled with the number place values.The number 295 is in the first row of the table. The 2 is in the hundreds column, the 9 is to the right in the tens column and the 5 is to the right again in the ones column. In the next row down is the number 29 point 5. The 2 is in the tens column, the 9 is in the ones column. There is a decimal point to the right of the 9, and then the 5 is to the right of that in the tenths column.
    As you can see from our place value chart. When 295 is divided by 10, 2 hundreds, 9 tens and 5 ones become 2 tens, 9 ones and 5 tenths. Dividing by 10 moved each number one place to the right.
    )
  3. \(9.72 × (10) = ?\) (
    Solution
    x
    Solution:
    \(97.2\)
    )
  4. \(54.6 ÷ 10 = ?\) (
    Video Solution
    x
    Solution: \(5.46\)
    Details:

    (Video Source | Transcript)
    )
  5. \(3.95 × 100 = ?\) (
    Video Solution
    x
    Solution: 395
    Details:

    (Video Source | Transcript)
    )
  6. \(17 ÷ 100 = ?\) (
    Solution
    x
    Solution:
    \(0.17\)
    )

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