To complete the statement, let's break it down step by step.
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Starting with the expression \((3 x _) + (4 x 100) \div 100\):
- When we divide by 100, it's equivalent to moving the decimal point two places to the left.
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We have:
- \((3 x _) + (4 x 100)\) represents the decimal number \(34\) (since \(3\) corresponds to \(3 x 10\) and \(4\) corresponds to \(4 x 1\)).
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The equation simplifies to: \[ \frac{(3 \cdot 10) + (4 \cdot 100)}{100} = \frac{30 + 400}{100} = \frac{430}{100} = 4.3 \]
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Therefore, in expanded form, we recognize that:
- The number we are considering consists of \(3\) representing the tenths place (hence \(3\) multiplied by \(10\)), and \(4\) in the hundredths place (or simply \(4\)).
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Given that dividing by \(100\) results in moving the decimal two places to the left, we see:
- The whole number becomes a decimal where \(4\) retains its position (now effectively representing \(4\)).
- The initial \(3\) was in the whole number place, and after division, this is shifted down to the tenths place.
So we can fill in the blanks as follows:
- Fill-in 1: \(10\) (to represent the position of \(3\))
- Fill-in 2: \(0.3\) (which is \(3\) divided by \(10\))
The completed statement would look like this: \[ {(3 \times 10) + (4 \times 100)} \div 100 \] \[ 0.3 + 4 \]
Thus, the digits shifted two places to the right because they're worth 100 times less than what they were before.
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