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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

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.

### Practice Problems

Evaluate the following expression:
1. $$86 × 10 = ?$$ (
Solution
Solution: 860
Details:

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
Solution: $$29.5$$
Details:

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
Solution:
$$97.2$$
)
4. $$54.6 ÷ 10 = ?$$ (
Video Solution
Solution: $$5.46$$
Details:

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

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

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