To express the number 20,109 in expanded notation, we break it down according to the place values of each digit:
- 2 is in the ten-thousands place, which represents \( 2 \times 10,000 \)
- 0 is in the thousands place, which represents \( 0 \times 1,000 \)
- 1 is in the hundreds place, which represents \( 1 \times 100 \)
- 0 is in the tens place, which represents \( 0 \times 10 \)
- 9 is in the ones place, which represents \( 9 \times 1 \)
So, the complete expression in expanded notation would be:
\[ 2 \times 10,000 + 0 \times 1,000 + 1 \times 100 + 0 \times 10 + 9 \times 1 \]
Given your expression \( 2x? + 1x100 + 9x10 \), to fit this into the expanded form of 20,109, the second term should correctly reflect the thousands place (which is 0).
Thus, it can be refitted to include:
- \( 2x10,000 \)
- \( 0x1,000 \)
- \( 1x100 \)
- \( 0x10 \)
- \( 9x1 \)
Expanding only focuses on correct place values leading to the completion of the expression. The part that requires completing for your expression is the thousands place:
So the correct placement for your expression is:
- \( 0 \) for the thousands place.
Therefore, the complete expression will correctly be: \[ 2x10,000 + 0x1,000 + 1x100 + 0x10 + 9x1 \]
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