Yes, expanded form can involve powers of 10. In mathematics, expressing a number in expanded form means breaking it down into the sum of its parts, particularly emphasizing the place value of each digit.
For example, the number 4,582 can be expressed in expanded form using powers of 10 as follows:
\[ 4,582 = 4 \times 1000 + 5 \times 100 + 8 \times 10 + 2 \times 1 \]
In terms of powers of 10, this can be written as:
\[ 4,582 = 4 \times 10^3 + 5 \times 10^2 + 8 \times 10^1 + 2 \times 10^0 \]
Here are the components broken down:
- \(4\) is in the thousands place, so it is \(4 \times 10^3\).
- \(5\) is in the hundreds place, so it is \(5 \times 10^2\).
- \(8\) is in the tens place, so it is \(8 \times 10^1\).
- \(2\) is in the ones place, so it is \(2 \times 10^0\).
This representation effectively shows the contribution of each digit to the overall number.
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