To convert the base-four number [tex]\(210_{\text{four}}\)[/tex] into a base-ten number, we follow these steps:
1. Identify the place values in the base-four number. Starting from the right, the place values are [tex]\(4^0\)[/tex], [tex]\(4^1\)[/tex], [tex]\(4^2\)[/tex], etc.
2. Each digit in the base-four number is multiplied by its corresponding power of 4.
So, we have:
[tex]\(2 \times 4^2 + 1 \times 4^1 + 0 \times 4^0\)[/tex]
3. Calculate the value of each term:
- [tex]\(2 \times 4^2 = 2 \times 16 = 32\)[/tex]
- [tex]\(1 \times 4^1 = 1 \times 4 = 4\)[/tex]
- [tex]\(0 \times 4^0 = 0 \times 1 = 0\)[/tex]
4. Sum these values:
[tex]\[32 + 4 + 0 = 36\][/tex]
Therefore, [tex]\(210_{\text{four}} = 36_{\text{ten}}\)[/tex].
