Question

Juliana wants to write the number 20,109 and expanded notation which of the following following would complete the expression 2x?+1x100+9x10

1,000
10 to the 4th power
100.000
10 to the third power
10,000

Answer 1

To write the number 20,109 in expanded notation, we break it down based on its place values:

- The first digit (2) is in the thousands place, which represents 2,000.
- The second digit (0) is in the hundreds place, which represents 0.
- The third digit (1) is in the tens place, which represents 10.
- The fourth digit (0) is in the ones place, which represents 0.
- The last digit (9) is in the ones place, which represents 9.

So, the expanded notation of 20,109 would be:

\[
2 \times 10^4 + 0 \times 10^3 + 1 \times 10^2 + 0 \times 10^1 + 9 \times 10^0
\]

Looking at your original expression:

\[
2x? + 1x100 + 9x10
\]

The "2x?" corresponds to the thousands place for 20,109, which is \(2 \times 10^4\).

The correct answer from your options that would complete this expression is:

**10 to the 4th power**.

So, the completed expression would be:

\[
2 \times 10^4 + 1 \times 100 + 9 \times 10
\]