Let's find the correct expanded notation for the number 12,536 by breaking it down step-by-step.
1. Recognize each digit's place value in the number 12,536:
- The first digit '1' is in the ten-thousands place.
- The second digit '2' is in the thousands place.
- The third digit '5' is in the hundreds place.
- The fourth digit '3' is in the tens place.
- The fifth digit '6' is in the ones place.
2. Write each digit multiplied by its corresponding place value:
- The digit '1' multiplied by 10,000:
[tex]\[
1 \times 10,000 = 10,000
\][/tex]
- The digit '2' multiplied by 1,000:
[tex]\[
2 \times 1,000 = 2,000
\][/tex]
- The digit '5' multiplied by 100:
[tex]\[
5 \times 100 = 500
\][/tex]
- The digit '3' multiplied by 10:
[tex]\[
3 \times 10 = 30
\][/tex]
- The digit '6' multiplied by 1:
[tex]\[
6 \times 1 = 6
\][/tex]
3. Combine these values to express the original number in its expanded notation form:
[tex]\[
(1 \times 10,000) + (2 \times 1,000) + (5 \times 100) + (3 \times 10) + (6 \times 1)
\][/tex]
When added together, these values equal the original number 12,536:
[tex]\[
10,000 + 2,000 + 500 + 30 + 6 = 12,536
\][/tex]
Therefore, the correct expanded notation for the number 12,536 is:
[tex]\[
(1 \times 10,000) + (2 \times 1,000) + (5 \times 100) + (3 \times 10) + (6 \times 1)
\][/tex]
